đề bài dou e

giúp j vậy bn?

4.

\(\dfrac{1}{a+3b}+\dfrac{1}{c+3}\ge\dfrac{4}{a+3b+c+3}=\dfrac{4}{\left(a+b+c\right)+2b+3}=\dfrac{4}{2b+6}=\dfrac{2}{b+3}\)

Tương tự:

\(\dfrac{1}{b+3c}+\dfrac{1}{a+3}\ge\dfrac{2}{c+3}\)

\(\dfrac{1}{c+3a}+\dfrac{1}{b+3}\ge\dfrac{2}{a+3}\)

Cộng vế:

\(\sum\dfrac{1}{a+3b}+\sum\dfrac{1}{a+3}\ge\sum\dfrac{2}{a+3}\)

\(\Rightarrow\sum\dfrac{1}{a+3b}\ge\sum\dfrac{1}{a+3}\) (đpcm)

Dấu "=" xảy ra khi \(a=b=c=1\)

d: Ta có: ƯCLN(a,b)=2

=>\(\left\{{}\begin{matrix}a=2x\\b=2y\end{matrix}\right.\)

\(a\cdot b=120\)

=>\(2x\cdot2y=120\)

=>\(x\cdot y=30\)

mà x,y là các số nguyên dương

nên \(\left(x,y\right)\in\left\{\left(1;30\right);\left(2;15\right);\left(3;10\right);\left(5;6\right);\left(6;5\right);\left(10;3\right);\left(15;2\right);\left(30;1\right)\right\}\)

=>\(\left(a,b\right)\in\left\{\left(2;60\right);\left(4;30\right);\left(6;20\right);\left(10;12\right);\left(12;10\right);\left(20;6\right);\left(30;4\right);\left(60;2\right)\right\}\)

\(A=\left(4x-1\right)\left(3x+1\right)-5x\left(x-3\right)-\left(x-4\right)\left(x-3\right)\)

\(=\left(4x-1\right)\left(3x+1\right)-\left(5x+x-4\right)\left(x-3\right)\)

\(=12x^2+4x-3x-1-6x^2+4x+18x-12\)

\(=18x^2+19x-13\)

á à láo tự lm đuy:)

chia 3 còn dư bao nhiêu vậy bn

Bài 3:

4.

$(x-3)(2x^2-x-4)=x(2x^2-x-4)-3(2x^2-x-4)$

$=(2x^3-x^2-4x)-(6x^2-3x-12)$

$=2x^3-7x^2-x+12$
5.

$(2x^2-x+3)(1-2x+2x^2)=2x^2(2x^2-2x+1)-x(2x^2-2x+1)+3(2x^2-2x+1)$

$=4x^4-6x^3+10x^2-7x+3$

6.

$(x-2)(2x-5)=2x^2-9x+10$

7.

$(x^2-x)(2x-3x^2)=x^2(x-1)(2-3x)$

$=x^2(5x-3x^2-2)=5x^3-3x^4-2x^2$
 

Bài 3:

8.

$(x+2)(x^2+3x)(4-x)$

$=(x+2)(4-x)(x^2+3x)=(2x-x^2+8)(x^2+3x)$

$=-x^4-x^3+14x^2+24x$

9. Giống câu 8

10.

$(3x+5)(-x^2+4x-2)=-(3x+5)(x^2-4x+2)$

$=-[3x(x^2-4x+2)+5(x^2-4x+2)]$

$=-(3x^3-7x^2-14x+10)$

Bài 4:

$A=5x(4x^2-2x+1)-2x(10x^2-5x-2)$

$=20x^3-10x^2+5x-(20x^3-10x^2-4x)$

$=9x=9.15=135$

$B=5x(x^2-3)+x^2(7-5x)-7x^2$

$=5x^3-15x+7x^2-5x^3-7x^2$

$=-15x=-15.(-5)=75$

$C=(x-2)(x^4+2x^3+4x^2+8x+16)$

$=x^4+2x^3+4x^2+8x+16$

$=x^3(x-3)+5x^2(x-3)+19x(x-3)+65x+16$

$=65x+16=65.3+16=211$