Câu hỏi của Sera Masumi

Question

1. Chứng tỏ rằng :

a) ( x + y ) $^3$ = x$^3$ + 3x$^2$y + 3xy$^2$ + y$^3$

b) ( x - y ) $^3$ = x$^3$ - 3x$^2$y + 3xy$^2$ - y$^3$

2 Tìm x :

a) x . ( 8x - 2 ) - 8x$^2$ + 12 = 0...

Nguyễn Thanh Hằng · Accepted Answer

1/ a/ $\left(x+y\right)^3=\left(x+y\right)\left(x+y\right)^2=\left(x+y\right)\left(x^2+2xy+b^2\right)=x^3+2x^2y+x^2y+xy^2+2xy^2+y^3=x^3+3x^2y+3xy^2+y^3$

b/ $\left(x-y\right)^3=\left(x-y\right)\left(x-y\right)^2=\left(x-y\right)\left(x^2-2xy+y^2\right)=x^3-2x^2y-x^2y+2xy^2+xy^2-y^3=x^3-3x^2y+3xy^2+y^3$2/

a/ $x\left(8x-2\right)-8x^2+12=0$

$\Leftrightarrow8x^2-2x-8x^2+12=0$

$\Leftrightarrow-2x+12=0$

$\Leftrightarrow x=6$

Vậy ...

b/ $\left(x-1\right)^3-x\left(x^2-3x+1\right)=18$

$\Leftrightarrow x^3-3x^2+3x-1-x^3+3x^2-x=18$

$\Leftrightarrow2x-1=18$

$\Leftrightarrow x=\dfrac{19}{2}$

Vậy...

3/ a, $25-x^2=5^2-x^2=\left(5-x\right)\left(5+x\right)$

b/ $4x^2-4x+1=\left(2x\right)^2-2.2x.1+1^2=\left(2x-1\right)^2$

c/ $9x^2+6xy+y^2=\left(3x\right)^2+2.3x.y+y^2=\left(3x+y\right)^2$Câu trả lời: 1/ a/ $\left(x+y\right)^3=\left(x+y\right)\left(x+y\right)^2=\left(x+y\right)\left(x^2+2xy+b^2\right)=x^3+2x^2y+x^2y+xy^2+2xy^2+y^3=x^3+3x^2y+3xy^2+y^3$