Question

The positive root of the equation $x^4 + x^2 - 2 = 0$ is ...........

Hint:

Quartic expressions often simplify using substitution $y = x^2$.

Answer 1

Correct Answer: 1

Step 1: Substitute $y = x^2$.
\[ x^4 + x^2 - 2 = 0 \Rightarrow y^2 + y - 2 = 0 \] Step 2: Factorize.
\[ (y + 2)(y - 1) = 0 \] \[ y = -2,\; y = 1 \] Step 3: Convert back to x.
Since $y = x^2$, \[ x^2 = 1 \Rightarrow x = \pm 1 \] Step 4: Positive root.
Positive root = 1.