Question

if x⁴ + 1\x² = 727 , find the value of:

(1) x² + 1\x²
(2) x - 1\x
(3) x³ - 1\x³​

Answer 1

Answer:

(x⁴+1/x⁴)+2 = 727+2

(x²+1/x²)²= 729

x²+1/x²= √729

x²+1/x²= √3×3×3×3×3×3

x²+1/x²= 27

(x²+1/x²)-2= 27-2

(x-1/x)²= 25

x-1/x= 5

(x-1/x)³= (5)³

x³-1/x³-3(x-1/x)= 35

x³-1/x³-15= 35

x³-1/x³= 35+15

x³-1/x³= 50