Question

Solve the quadratic equation : 3x⁴ - 13x² +10 = 0.

Answer 1

3x⁴ - 13x² +10 = 0

∴ 3(x²)² - 13x² + 10 = 0

[∵(a^m)ⁿ = a^m×n]  

Substituting x² = m we get, 

3m² - 13m + 10 = 0

∴ 3m2 - 3m - 10m + 10 = 0 

∴3m (m - 1) - 10 (m -1)= 0

∴ (m – 1) (3m – 10) = 0

∴ m – 1 = 0 or 3m – 10 = 0

∴ m = 1 or 3m = 10

∴ m = 1 or m = `10/3`

Resubstituting m = x²  we get,

x² = 1 or x² = `10/3` 

∴ x = ±√1  or x = ±`√(10/3)`

∴ x = ±1 or x = ±`√(10/3)`