Solve x ^ 2 + 4/(x ^ 2) = 5 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$x^{2}+\frac{4}{x^{2}}=5$$

Solve for x

$x=-1$
$x=1$
$x=2$
$x=-2$

Steps Using the Quadratic Formula

Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $x^{2}$.

$$x^{2}x^{2}+4=5x^{2}$$

To multiply powers of the same base, add their exponents. Add $2$ and $2$ to get $4$.

$$x^{4}+4=5x^{2}$$

Subtract $5x^{2}$ from both sides.

$$x^{4}+4-5x^{2}=0$$

Substitute $t$ for $x^{2}$.

$$t^{2}-5t+4=0$$

All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. Substitute $1$ for $a$, $-5$ for $b$, and $4$ for $c$ in the quadratic formula.

$$t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 1\times 4}}{2}$$

Do the calculations.

$$t=\frac{5±3}{2}$$

Solve the equation $t=\frac{5±3}{2}$ when $±$ is plus and when $±$ is minus.

$$t=4$$ $$t=1$$

Since $x=t^{2}$, the solutions are obtained by evaluating $x=±\sqrt{t}$ for each $t$.

$$x=2$$ $$x=-2$$ $$x=1$$ $$x=-1$$