Câu hỏi của le thi yen chi

Question

bài tập 1: tìm x, biết

a) (x - 3)(x + 3) = (x - 2)2 - 1

b) (2x - 1)2 = (2x +5)(2x - 5) + 2

c) (x + 1)3 = x2(x - 2) + 5(x2 - 1

d) (x2 - 3x + 9)(x + 3) = (x - 2)3 + (3x - 1)(2x + 3)

Nháy >.< · Accepted Answer

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

$\Leftrightarrow x^2-9=x^2-4x+4-1$

$\Leftrightarrow4x=12$

$\Leftrightarrow x=3$

b) $\left(2x-1\right)^2=\left(2x+5\right)\left(2x-5\right)+2$

$\Leftrightarrow4x^2-4x+1=4x^2-25+2$

$\Leftrightarrow4x=24$

$\Leftrightarrow x=6$

c) $\left(x+1\right)^3=x^2\left(x-2\right)+5\left(x^2-1\right)$

$\Leftrightarrow x^3+3x^2+3x+1=x^3-2x^2+5x^2-5$

$\Leftrightarrow3x=-6$

$\Leftrightarrow x=-2$

d) $\left(x^2-3x+9\right)\left(x+3\right)=\left(x-2\right)^3+\left(3x-1\right)\left(2x+3\right)$

$\Leftrightarrow x^3+3^3=x^3-6x^2+12x-8+6x^2+7x-3$

$\Leftrightarrow x^3+27=x^3+19x-11$

$\Leftrightarrow19x=38$

$\Leftrightarrow x=2$Câu trả lời: a) $\left(x-3\right)\left(x+3\right)=\left(x-2\right)^2-1$