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Answer:
given: x+1/x = 4
to evaluate x⁴+1/x⁴
Step-by-step explanation:
(x+1/x)² = x²+1/x²+2
=> 4² = x²+1/x²+2
=> 16-2 = x²+1/x²
=> x²+1/x² = 14............1
square equation 1
=> (x²+1/x²)² = x⁴+1/x⁴+2
[ (a+1/a)² = a² + 1/a² + 2*a*1/a => a² + 1/a² + 2 ]
=> 14² = x⁴+1/x⁴+2
=> 196 = x⁴+1/x⁴+2
=> 196 - 2 = x⁴+1/x⁴
=> x⁴+1/x⁴ = 194
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