Question

Gi ải phương trình:

(x² + 2x - 1)² - 9 = 0

Phân tích thành nhân tử: x² + 2x - 4

Answer 1

\(\Leftrightarrow\left(x^2+2x-1+3\right)\left(x^2+2x-1-3\right)=0\)

\(\Leftrightarrow\left(x^2+2x+2\right)\left(x^2+2x-4\right)=0\)

\(\Rightarrow x^2+2x-4=0\)

\(\Leftrightarrow x\left(x+2\right)=4\)

\(\Rightarrow\)

x	1	-1	2	-2	4	-4
x+2	4	-4	2	-2	1	-4

\(\Rightarrow x\in\left\{\pm1,\pm2,\pm4,-3,0,-6\right\}\)

Answer 2

\(x^2+2x-4\\ =\left(x^2+2x+1\right)-5\\ =\left(x+1\right)^2-5\\ =\left(x+1-\sqrt{5}\right)\left(x+1+\sqrt{5}\right)\)