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If x^4+1/(x^4)=194 , find x^3+1/(x^3),x^...

If `x^4+1/(x^4)=194 ,` find `x^3+1/(x^3),x^2+1/(x^2)` and `x+1/x`

Text Solution

Verified by Experts

Given,
⇒`'x⁴ + 1/x⁴ =194
⇒x⁴ + 1/x⁴ +2 =194+2
⇒(x² + 1/x²)² =196
∴ x² + 1/x² =14'.......(ii)
⇒'x² + 1/x² +2 =16
⇒(x + 1/x)²=16
∴ x+ 1/x =4.......(iii)
⇒(x+ 1/x)³ =x³ + 1/x³ +3(x+ 1/x)
∴ x³ + 1/x³ =52'........(i)`
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