Question

Sin 36° is root of equation whose coefficients are rational is given by

(1) 16x⁴ + 20x² - 5 = 0

(2) 16x⁴ + 20x² + 5 = 0

(3) 16x⁴ - 20x² + 5 = 0

(4) 8x⁴ - 20x² + 5 = 0

Answer 1

(3) 16x⁴ - 20x² + 5 = 0

sin 36° = x = \(\frac{\sqrt{10}-2\sqrt{5}}{4}\)

16x² = 10 -2√5

(16x²-10)² = 20 

(8x² - 5)² = 5 

64x⁴ + 25 - 80x² - 5 = 0 

64x⁴ - 80x² + 20 = 0 

16x⁴ - 20x² + 5 = 0