Question

(x-1/x) find the values of:x+1/x b)x²+1/x² c)x⁴-1/x⁴​

Answer 1

x + 1/x = 4……………(1)

Squaring both sides.

X^2 + 1/x^2+ 2 = 16

or. x^2 + 1/x^2= 14.

Again squaring both sides.

x^4 +1/x^4 +2 = 196.

or. x^4 + 1/x^4 = 194. Answer.

Answer 2

Step-by-step explanation:

suppose x-1/x = a

x-1/x = a

=> (x-1/x)² = a²

=> x²+1/x²-2*x*1/x = a²

=> x²+1/x²-2 = a²

=> x²+1/x² = a²+2

a) (x+1/x)²

= x²+1/x²+2*x*1/x

= x²+1/x²+2

= a²+2+2 (x²+1/x² = a²+2)

= a²+4

(x+1/x)² = a²+4

=> x+1/x = √(a²+4)

b) x-1/x = a

=> (x-1/x)² = a²

=> x²+1/x²-2*x*1/x = a²

=> x²+1/x²-2 = a²

=> x²+1/x² = a²+2

c) x⁴-1/x⁴

= (x²-1/x²)(x²+1/x²)

= (x-1/x)(1+1/x)(x²+1/x²)

= a*√(a²+4)*(a²+2)

using formula (x-y)² = x²+y²-2*x*y

(x+y)² = x²+y²+2*x*y

x²-y² = (x+y)(x-y)