Question

3x⁴ – 13x² + 10 = 0

Answer 1

Given: 3x⁴ – 13x² + 10 = 0
Let x² = m. Then, the equation can be written as:
3m² – 13m + 10 = 0
On splitting the middle term –13m as –3m – 10m, we get:
3m² – 3m – 10m + 10 = 0
$\Rightarrow$ 3m(m – 1) –10(m – 1) = 0
$\Rightarrow$ (m – 1)(3m – 10) = 0
$\Rightarrow$ m – 1 = 0 or 3m – 10 = 0
$\Rightarrow$ m = 1 or m = $\frac{10}{3}$
On substituting m = x², we get:
x² = 1 or x² = $\frac{10}{3}$
$\Rightarrow$ x = ±1 or x = ± $\sqrt{\frac{10}{3}}$
Thus, the solutions of the given equation are ±1, ± $\sqrt{\frac{10}{3}}$