If x+1\x=9,find the value of x4+1\x4
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Given : x + 1/x = 9
To Find : Value of x⁴ + 1/x⁴
Solution:
x + 1/x = 9
Squaring both sides
=> x² + 1/x² + 2x(1/x) = 81
=> x² + 1/x² + 2 = 81
=> x² + 1/x² = 79
Squaring both sides again
=> x⁴ + 1/x⁴ + 2x²(1/x²) = 79²
( 79² = (80 - 1)¹ = 6400 + 1 - 2(80)(1) = 6241 )
=> x⁴ + 1/x⁴ + 2 = 6241
=> x⁴ + 1/x⁴ = 6239
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