Question

Giải các phương trình sau:

a \(x^4-x^2-56=0\)

b \(\left(x-2\right)^4+\left(x+2\right)^4=32\)

c \(\left(x+3\right)^4+\left(x+5\right)^4=16\)

d \(\left(6-x\right)^4+\left(8-x\right)^4=80\)

Answer 1

a) \(x^4-x^2+\dfrac{1}{4}-\dfrac{225}{4}=0\\ \left(x^2-\dfrac{1}{2}\right)^2-\dfrac{15}{2}^2=0\\ \left(x+7\right)\left(x-8\right)=0\\ \left[{}\begin{matrix}x=8\\x=-7\end{matrix}\right.\)

Vậy x = 8 hoặc x = -7

 

Answer 2

a: Ta có: \(x^4-x^2-56=0\)

\(\Leftrightarrow x^4-8x^2+7x^2-56=0\)

\(\Leftrightarrow\left(x^2-8\right)\left(x^2+7\right)=0\)

\(\Leftrightarrow x^2-8=0\)

hay \(x\in\left\{2\sqrt{2};-2\sqrt{2}\right\}\)