Question

if x+1/x=4 and find the value of x^4-1/x^4

Answer 1

112√3

x + 1/x = 4 ( squaring on both sides )

( x + 1/x ) ² = 4²

x ² + 1/ x² = 16 - 2

x ² + 1 / x². = 14. ---- ( 1 ). ( SOBS )

( X ² + 1 / X ² ) ². = 14 ²

X ⁴ + 1 / X ⁴ = 14 ² - 2 = 194

LET ( X ² - 1 / X ² ) ² = X ⁴ + 1 / X ⁴ - 2

( X ² - 1 / X ² ) ² = 194 - 2 = 192

( X ² - 1 / X ² ) = √ 192 = 8√3

NOW ( X² + 1/X ² ) ( X² - 1/X ² ) = 14 × 8√3

SO, ( X ⁴ - 1 / X ⁴ ) = 112 √3