Question

x+1/x=2√2 find x^4+1/x^4​

Answer 1

Step-by-step explanation:

x+1/x=2√2

squarring on both side

(x+1/x)²=(2√2)²

again squarring on both side

[(x+1/x)²]²=[2√2)²]

[x²+1/x²+2)]²=(8)²

(x²)²+(1/x²)²+(2)²+2+4/x²+4x²=64

x⁴+1/x⁴+4+2+4/x²+4x²=64

x⁴+1/x⁴+6+4/2√2+8√2=64

x⁴+1/x⁴+4/2√2*√2/√2+8√2=64

x⁴+1/x⁴=64-9√2