Solve the equation: x^4 - x^2 - 2 =0

Question

Solve the equation:

`x^4 - x^2 - 2 =0`

Answer 1

±2

Explanation:

This is a biquadratic equation, we must turn it into a quadratic one first before we solve it. So, let's say that x⁴ = y², therefore

`y = √(x)`

and we turn it into the following quadratic equation:

y² - y - 2 = 0

then we solve it the way we solve a normal quadratic equations and find the roots:

D = 1 + 8 = 9

y1,2 = 1 ± 3 = 4, -2

`√(x) = y`

We cannot find the square root of -2, so the solutions are only -2 and 2(because square root of 4 is equal to ±2)