Question

Cho A= \(\left(\frac{1-x^3}{1-x}+x\right)\)\(\left(\frac{1+x^3}{1+x}-x\right)\)

a, Rút gọn A

b, Tìm x để A = 64

Answer 1

Lời giải:
a)

ĐKXĐ: $a\neq \pm 1$

\(A=\left[\frac{(1-x)(1+x+x^2)}{1-x}+x\right]\left[\frac{(1+x)(1-x+x^2)}{1+x}-x\right]\)

\(=(1+x+x^2+x)(1-x+x^2-x)\)

\(=(x^2+2x+1)(x^2-2x+1)=(x+1)^2(x-1)^2=(x^2-1)^2\)

b)

\(A=64\)

\(\Leftrightarrow (x^2-1)^2=64\)

\(\Rightarrow \left[\begin{matrix} x^2-1=8\\ x^2-1=-8\end{matrix}\right.\Rightarrow \left[\begin{matrix} x^2=9\\ x^2=-7(\text{vô lý})\end{matrix}\right.\)

\(\Rightarrow x=\pm 3\) (đều thỏa mãn)

Vậy........