Question

Solve the following equations.

x⁴ – 3x² + 2 = 0

Answer 1

Given: x⁴ – 3x² + 2 = 0
Let x² = m. Then, the equation can be written as:
m² – 3m + 2 = 0
On splitting the middle term –3m as –m – 2m, we get:
m² – m – 2m + 2 = 0
$\Rightarrow$ m(m – 1) –2(m – 1) = 0
$\Rightarrow$ (m – 1)(m – 2) = 0
$\Rightarrow$ m – 1 = 0 or m – 2 = 0
$\Rightarrow$ m = 1 or m = 2
On substituting m = x², we get:
x² = 1 or x² = 2
$\Rightarrow$ x = ±1 or x = ±$\sqrt{2}$
Thus, the solutions of the given equation are ±1 and ±$\sqrt{2}$.