Mathematics: Math question! Please help.

2:5Step-by-step explanation:...

Math question! Please help. - id5117030, akiib

eddie2468

18.01.2022

The value of x is x=1, x=-1

Explanation:

The expression is $\sqrt{2 x^{2}-1}=x$

Square both sides of the equation, we get,

$2 x^{2}-1=x^{4}$

Switch sides,

$x^{4}=2 x^{2}-1$

Subtracting both sides by $2 x^{2}$ ,

$x^{4}-2 x^{2}=-1$

Adding both sides by 1,

$x^{4}-2 x^{2}+1=0$

Let us rewrite the equation as $u=x^{2}$ and $u^{2}=x^{4}$

Thus, we have,

$u^{2}-2 u+1=0$

Simplifying using quadratic formula,

$u=\frac{-(-2) \pm \sqrt{(-2)^{2}-4 \cdot 1 \cdot 1}}{2 \cdot 1}$

Simplifying, we get,

$u=\frac{-(-2)}{2 \cdot 1}$

u=1

Substituting u=1 in $u=x^{2}$ , we get,

$x^{2} =1$

x=1, x=-1

Thus, the value of x is x=1, x=-1

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