Question

of x+1/x=
$\sqrt{p}$
, find the value of ( x^4+1/x^4)​

Answer 1

Answer:

given : x + 1/x = √p

to evaluate x⁴ + 1/x⁴

x + 1/x = √p

squaring both sides

(x + 1/x)² = (√p)²

=> x² + 1/x² + 2*x*1/x = p

=> x² + 1/x² + 2 = p

=> x² + 1/x² = p - 2

again squaring both sides

=> (x² + 1/x²)² = (p - 1)²

=> x⁴ + 1/x⁴ + 2 * x² * 1/x² = p² - 2p + 1

=> x⁴ + 1/x⁴ + 2 = p² - 2p + 1

=> x⁴ + 1/x⁴ = p² - 2p + 1 - 2

=> x⁴ + 1/x⁴ = p² - 2p - 1