Bài tập 110 trang 42 SGK Toán 6 Tập 1

Chứng minh rằng :

a, Trong 3 số tự nhiên liên tiếp , có 1 và chỉ 1 số chia hết cho 3 .

b, Trong 2 số chẵn liên tiếp , có 1 và chỉ 1 số chia hết cho 4 .

Tính :

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 . 0 + 1 = ?

Tìm a \(\in\) N biết 355chia cho a dư 13 và 836 chia cho a thì dư 8

Tìm x; y \(\in\) N biết ( x + 1 ) . ( 2y - 5 ) = 143

Cho A= 4 + 4\(^2\) + 4\(^3\) +...............+ 4\(^{23}\) + 4\(^{24}\). Chứng minh rằng

A chia hết cho 20

A chia hết cho 21

A chia hết cho 420

Tìm số tự nhiên nhỏ nhất sao cho chia nó cho 17 thì dư 5; chia nó cho 19 thì dư 12

Chiến thắng Đống Đa vào mùa xuân năm 1789. Trong hệ đếm CAN CHI, năm đó là năm nào?

so sánh :

27^10 . 16^9; 12^48

Chứng minh rằng:

5^200+5^199+5^198 chia hết cho 31

1,Thực hiện phép tính:

1 - 2 + 3 - 4 + 5 - 6 + ..........+2011 - 2012

Bài 1 khi chia a cho 9 có số dư là 6 . Hỏi a có chia hết cho 3 ko? Cho 9 ko?

bài 2:Số 6⁵ - 9² có chia hết cho 3k ko? ( lưu ý trên 3k có dấu gạch ngang)

Tìm N để (3N+1) (N-1)

Đang gấp đúng mình tick cho

Thay dấu * bởi chữ số thích hợp để số 59*

a. Chia hêt cho 2

b. chia hết cho 5

c. chia hết cho cả 2 và 5

d. Ko chia hết cho cả 2 và 5

e. Chia hết cho 3 và ko chia hết cho 9

g. Chia hết cho 9

Chứng minh rằng A\(⋮\)7

A=\(2^1+2^2+2^3+2^4+.....+2^{59}+2^{60}\)

2. a) Tìm n thuộc N để n^5+1 chia hết cho n^3+1

b) Tìm n thuộc Z để n^5+1 chia hết cho n^3+1

3. Tìm số nguyên n sao cho:

a) n^2+2n-4 chia hết cho 11

b) 2n^3+n^2+7n+1chia hết cho 2n-1

c) n^4-2n^3+2n^2-2n+1 chia hết cho n^4-1

d) n^3-n^2+2n+7 chia hết cho n^2+1

Cho biểu thức :

A = \(\dfrac{1+5+5^2+..........+5^9}{1+5+5^2+............+5^8}\)

B = \(\dfrac{1+3+3^2+............+3^9}{1+3+3^2+............+3^8}\)

Giúp mình nhanh với .

Tìm x \(\in\)N

a) x + ( x + 1 ) + ( x + 2 ) + .....+ ( x + 30 ) = 1240

b) 1 + 2 + 3 +........+ x = 210

Thực hiện các phép tính sau bằng cách hợp lí nhất:

a) 19 + 19 + 19 +.......... + 19 + 77 + 77 + 77 +........+ 77

( 23 số hạng 19) ( 19 số hạng 77 )

b) 1000! . ( 456 . 789789 - 789 . 456456 )

1. Bỏ dấu ngoặc rồi thu gọn biểu thức:

a)A=(a+b)-(a-b)+(a-c)-(a+c)

Học kì 2, lớp 6A dự định bỏ tiền heo đất để ăn liên hoan cuối năm. Mỗi ngày lớp bỏ 40.000 đồng. Nếu lớp bắt đầu bỏ từ tháng 1 đến tháng 4 lớp sẽ được bao nhiêu tiền. (Giả sử trung bình mỗi tháng có 30 ngày)

Tìm n, biết

\(n^2+5⋮n+1\)

Cho 894a2b chia hết cho tất cả các số 2, 3, 5, 6, 9, 15

Tim x biet

\(\left(2x-1\right)^2-2=30\)

Một người đi xe đạp từ A đến B tron g một thời gian qui định và với vận tốc xác định . Nếu người tăng vận tốc 3 km/h thì sẽ đến sớm 1h . Nếu người đó giảm vận tốc 2km/h thì đến B muộn 1h . Tính khoảng cách AB , vận tốc và thời gian đi của người đó .

Đề bài: Phân tích đa thức thành nhân tử: x^2 -y^2 + 6xy + 9.

Cho 0<a≤b≤c .chứng minh rằng

\(\dfrac{a}{b}+\dfrac{b}{c}+\dfrac{c}{a}\)≥\(\dfrac{b}{a}+\dfrac{c}{b}+\dfrac{a}{c}\)

bài 1: một bác thợ lập kế hoạch lập một số sản phẩm, theo đó mỗi ngày bác phải làm 10 sản phẩm. Do cải tiến kĩ thuật nên bác làm được 14 sản phẩm mỗi ngày . Vì vậy, không nhữg hoàn thành xong trước 2 ngày so với kế hoạch mà còn thêm được 12 sản phẩm.

Hỏi theo kế hoạch tổng số sản phẩm mà bác thợ phải làm là bao nhiêu?

giúp mình nhá! mình cần gấp.

Rút gọn:

\(a\left(b+c-a\right)^2+b\left(c+a-b\right)^2+c\left(a+b-c\right)^2+\left(b+c-a\right)\left(c+a-b\right)\left(a+b-c\right)\)

lưu ý đg có làm kiểu hay là rồi rút gọn nha mấy bn có cái háng ngồi không :)

mà k làm đc thì cho lên câu hỏi hay giùm mk nha ace CTV :3

lẹ nha tối nay thôi T.T

một xe ô tô dự định đi từ A đến B với vận tốc 48km/h . sau khi đi được 1 h thì xe bị hỏng phải dừng lại sửa 15 phút . do đó để đến B đúng h dự định ô tô phải tăng vận tốc thêm 6km/h. tính quãng đường AB?

cho a, b là 2 số dương . Chứng minh rằng:

\(\left(1+\dfrac{a}{b}\right)^5+\left(1+\dfrac{b}{a}\right)^5\) ≥ 64

Tìm min 2x²+y²-2x-4y+2018-2xy

Tìm GTLN:

a) A=-x² +6x -5

b) B=-x²-3x+4

c) C=-3x²+2x -1

d) D=ax² + bx + c ( với a<0 ,abc là hằng số )

Cho biểu thức A =\(\dfrac{x+2}{x+3}\) - \(\dfrac{5}{x^2+x-6}\) + \(\dfrac{1}{2-x}\)

a, Tìm điều kiện của x để A có nghĩa

b, Rút gọn A

c, Tìm x để A=-3/4

d, Tìm x để biểu thức A có giá trị nguyên

e, Tính giá trị của biểu thức A khi x²-9=0

A=\(2^1+2^2+2^3+...+2^{59}+2^{60}\)

CMR : A⋮7

giải phương trình

\(\dfrac{x}{2\left(x-3\right)}+\dfrac{x}{2\left(x+1\right)}=\dfrac{2x}{\left(x+1\right)\left(x-3\right)}\)

Phân tích đa thức sau thành nhân tử : A=(a+1)(a+3)(a+5)(a+7)+15

Tìm x,biết:

\(8\times6+288:\left(x-3\right)^2=50\\ \)

1. Cho biểu thức M =2/n-1 (n khác 1). Tìm tất cả các số nguyên n để M có giá trị là số nguyên.

x²-4x+4=x-2 giải phương trình

a) Tìm giá trị nhỏ nhất: A= 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Cho a, b, c thỏa mãn: \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=0\)

Tính giá trị biểu thức: A=\(\dfrac{b+c}{a}+\dfrac{c+a}{b}\dfrac{a+b}{c}\)

Cho a+b+c= 1, chứng minh rằng: a²+b²+c²\(\ge\)^{\(\dfrac{1}{3}\)}

Cho 3 số a,b,c thỏa mãn a+b+c=2.Tìm giá trị nhỏ nhất của biểu thức: \(A=a^2+b^2+c^2\)

Cho a,b,c là số đo ba cạnh của tam giác

Chứng minh rằng \(1< \dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}< 2\)

Tìm x để biểu thức A=3x2−8x+6x2−2x+13x2−8x+6x2−2x+1đạt giá trị nhỏ nhất. Tính giá trị nhỏ nhất đó.

làm giùm mk nka mk sắp thi òi!!!!!!!!!!!

Tìm x để biểu thức A=\(\dfrac{3x^2-8x+6}{x^2-2x+1}\)đạt giá trị nhỏ nhất. Tính giá trị nhỏ nhất đó.

làm giùm mk nka mk sắp thi òi!!!!!!!!!!!

Giải các BPT sau :

a) 2x - 3 / 35 + x (x - 2) / 7 < x² / 7 - 2x - 3 / 5

b) 3x - 2 / 4 < 3x + 3 / 6

So sánh: \(\sqrt{1969}\)+\(\sqrt{1971}\) và 2\(\sqrt{1970}\)

mình nhờ các bạn giải hộ vài bài với, mình xin cảm ơn rất nhiều

1. Giải phương trình

a) (x+5)(2x+1) - x² + 25 = 0

b 3x/x-2 - x/x-5 + 3x/(x-2)(x-5) = 0

2 cho phương trình ẩn x

x+1/x+2+m = x+1/x+2-m

a) giải phương trình khi m = -3

b) tìm các giá trị m sao cho phương trình nhận x=3 làm nghiệm

Cho tam giác ABD vuông tại B, có AB= 6cm, AD= 10 cm. Trên cạnh AD lấy điểm C sao cho AC= AB

Cm: BC là tia phân giác của góc EBD

Cho A=\(\dfrac{x-5}{2x+1}\). Tìm \(\in\)Z để A nguyên.

Giải BPT

3x - 2 / 4 > 3x + 3 / 6

Tìm giá trị nhỏ nhất của biểu thức A=\(\dfrac{-5}{x^2-2x+3}\)

Giải phương trình sau:

|2x—5|+|1—3x|+|x|=7

Một xe máy đi từ A đến B dài 35km. Lúc về đi bằng đường khác dài 42km với vận tốc kém hơn lượt đi là 6km/h. Tinh vận tốc lượt đi, lượt về, biết thời gian về bằng 2/3 thời gian đi..

Lúc 6h sáng, một xe máy khởi hành từ A đến V. Sau đó 1h, một ôtô cũng xuất phát từ A đến B với vận tốc trung bình lớn hơn vận tốc của xe máy 20km/h. Cả 2 xe đến B đồng thời lúc 9h30' sáng cùng ngày. Tính độ dài quãng đường AB, và vận tốc trung bình của xe máy

Cho 2 số x,y thoả mãn điều kiện 3x+y=1. Tìm GTNN của biểu thức M= 3x^2 + y^2

giai pt này giùm mik đê:\(\dfrac{2x-5}{x-2}-\dfrac{3x-5}{x-1}=-1\)

1/ cho 3 số tự nhiên a, b ,c thỏa mãn a+b+c=2. tìm giá trị nhỏ nhất của biểu thức:

A= a² + b² + c² =0

giúp mk với

Bài 1: Một ô tô dự định đi từ A đến B với vận tốc 48km/h. Sau khi đi được 1 giờ thì xe bị hỏng phải dừng lại sửa 15 phút. Do đó để đến B đúng giờ dự định ô tô phải tăng tốc thêm 6km/h. Tính quăng đường AB

Bài 2: Một ca nô xuôi dòng từ A đến B hết 1h 20 phút và ngược dòng hết 2h. Biết vận tốc dòng nước là 3km/h. tính vận tốc riêng của ca nô

Bài 3: Một tổ sản xuất theo kế hoạch mỗi ngày phải sản xuất 50 sản phẩm. Khi thực hiện tổ đã sản xuất được 57 sản phẩm một ngày. Do đó đã hoàn thành trước kế hoạch 1 ngày và còn vượt mức 13 sản phẩm. Hỏi theo kể hoạch tổ phải sản xuất bao nhiêu sản phẩm

Bài 4: Số học sinh giỏi lớp 8/1 bằng 3/4 số học sinh khá và nhiều hơn học sinh trung bình là 5 học sinh? Biết lớp có 40 học sinh gồm giỏi khá trung bình. Tinh số học sinh giỏi khá trung bình

Bài 5: Trong tháng Giêng hai tổ công nhân may đc 800 chiếc áo. Tháng 2 tổ 1 vượt mức 15%, tổ 2 vượt mức 20% do đó cả hai tổ sản xuất được 945 cái áo. Tính xem trong tháng đầu mỗi tổ may được bao nhiêu cái áo

Bài 6: Hai lớp 8A và 8B có tổng cộng 94 học sinh biết rằng 25% số học sinh 8A đạt loại giỏi, 20% số học sinh 8B và tổng số học sinh giỏi hai lớp là 21 học sinh. Tinh số học sinh mỗi lớp

Chứng minh rằng:

a, \(a^2\)+\(b^2-2ab\ge0\)

b,\(\dfrac{a^2+b^2}{2}\ge ab\)

c,\(a\left(a+2\right)< \left(a+1\right)^2\)

d,\(m^2+n^2+2\ge2\left(m+n\right)\)

e, \(\left(a+b\right)\left(\dfrac{1}{a}+\dfrac{1}{b}\right)\ge4\)(với a > 0, b > 0)

Cho a,b,c là các số thực dương thỏa mãn \(a+b+c=1\)

chứng minh rằng \(\dfrac{ab+c}{c+1}+\dfrac{bc+a}{a+1}+\dfrac{ac+b}{b+1}\le1\)

Cho 3 số a,b,c thỏa mãn \(a+b+c=2017\) và \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=\dfrac{1}{2017}\)

Chứng minh rằng ít nhất một trong ba số a,b,c bằng 2017

Chứng minh với mọi số x thì:

a, căn của 3x² + 6x + 12 cộng căn của 5x⁴ - 10x² + 9 lớn hơn hoặc bằng 5

b, căn của 3x² + 6x + 12 cộng căn của 5x⁴ - 10x² + 9 bằng 3 - 4x - 2x²

Giải phương trình

a, \(x^4+3x^3+4x^2+3x+1=0\)

b, \(x^6-x^5+x^4-x^3+x^2-x+\dfrac{3}{4}=0\)

cho a+b+c=1; a, b, c >0 .

tìm Mmin=1/a+1/b+1/c

Một ô tô dự định đi từ A - B với vận tốc 40km/h. Lúc đầu đi với vận đó , khi còn 60km nữa được nửa đường thì người lái xe tăng tốc thêm 10km/h nên đã đến B sớm hơn dự định 1h. Tính quãng đường AB

cho phương trình ẩn x sau ( 2x+m)(x-1)-2\((x)^{2}\)+mx+m-2=0

tìm các giá trị của m để phương trình có nhgiệm là một số không âm

Cho a,b,c>0 và a×b×c=1. Tìm GTNN của bt sau:

P=(a+1)(b+1)(c+1)

\(A=\left(\dfrac{x}{x^2-4}+\dfrac{2}{2-x}+\dfrac{1}{x+2}\right):\left(x-2+\dfrac{10-x^2}{x+2}\right)\)
a)Rút gọn
b) Tính giá trị x để A < 0

Tìm GTNN của bt:

A= x²-7x+11

Câu 1: a, Một người đi bộ từ A đến B với vận tốc 8km/h. Lúc về người đó đi với vận tốc 10km/h nên thời gian về ít hơn thời gian đi là 30 phút. Tính quãng đường AB.

b, giải bất phương trình sau và biểu diễn tập nghiệm trên trục số.

\(\dfrac{12x+1}{12}>=\dfrac{9x+3}{3}-\dfrac{8x+1}{4}\)

Tính\(\left(2x-3\right)^2=\left(2x-3\right)\left(x+1\right)\)

Cho biểu thức :
\(A=\dfrac{3x+15}{x^2-9}+\dfrac{1}{x+3}-\dfrac{2}{x-3 }\)
a) rút gọn A
b) Tìm x để \(A=\dfrac{1}{2}\)

Tìm GTNN của

B=\(5-\dfrac{\left(X+19\right)^2-325}{3\left(x+1\right)^2+6}\)