Question

if x+1/x=4 evaluate x2+1/x2 and x4+1/x4​

Answer 1

Hie!!

1)

( x + 1/x ) = 4

Squaring on both sides we have

( x + 1/x )² = 4²

x² + 1/x² + 2 = 16

Becoz ( a + b )² = a² + b² + 2ab

x² + 1/x² = 14

So, x² + 1/x² = 14

2) Find x⁴ + 1/x⁴

x² + 1/x² = 14

SQUARING ON BOTH SIDE'S WE HAVE

( x² + 1/x² )² = (14)²

x⁴ + 1/x⁴ + 2 = 196

x⁴ + 1/x⁴ = 194

So, x⁴ + 1/x⁴ = 194

Answer 2

Answer:

Given: (x+1/x)=4

we know that

(x+1/x)²=x²+1/x² + 2

Putting:(x+1/x)=4

Then:

⇒(4)²=x²+1/x² + 2

⇒16=x²+1/x² + 2

⇒14=x²+1/x²

Step-by-step explanation: