Question

If x+1/x=9 find the value of x4+1/x4​

Answer 1

Step-by-step explanation:

x+1/x=9

x+1=9x

1=9x-x

1=8x

1/8=x

x⁴+1/x⁴

(1/8)⁴+1/(1/8)⁴

1/4096+1/1/4096

1/0.0002

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Answer 2

Step-by-step explanation:

x+1/x=9

Squaring both sides,

(x+1/x)²=(9)²

(x)²+1/x²+2×x×1/x=81

x²+1/x²+2=81

x²+1/x²=81-2

x²+1/x²=79

Now,

(x²+1/x²)=79

Squaring both sides,

(x²+1/x²)²=(79)²

(x²)²+(1/x²)²+2×x²×1/x²=6241

x⁴+1/x⁴+2=6241

x⁴+1/x⁴=6241-2

x⁴+1/x⁴=6239