Question

Solve the following by reducing them to quadratic equations:
x⁴ - 26x2 + 25 = 0

Answer 1

Given x⁴ - 26x² + 25 = 0
Putting x² = y, the given equation reduces to the form y² - 26y + 25 = 0
⇒ y² - 25y - y + 25 = 0
⇒ y(y - 25) -1(y- 25) = 0
⇒ (y - 25) (y - 1) = 0
⇒ y - 25 = 0 or y - 1 = 0
⇒ y = 25 or y = 1
∴  x² = 25
⇒ x = ± 5
or
x² = 1
x = ±1
Hence, the required roots are ±5, ±1.