Question

if x-1/x=5, find the value of x4+ 1/x4​

Answer 1

Answer:

727

Step-by-step explanation:

⇒ x - 1 / x = 5

Square on both sides:

⇒ ( x - 1 / x )^2 = 5^2  

   Using ( a - b )^2 = a^2 + b^2 - 2ab

⇒ ( x )^2 + ( 1 / x )^2 - 2( x * 1 / x ) = 25

⇒ x^2 + 1 / x^2 - 2( 1 ) = 25

⇒ x^2 + x^2 = 25 + 2

⇒ x^2 + 1 / x^2 = 27

 Again, square on both sides:

⇒ ( x² + 1 / x² )² = 27²

⇒ x⁴ + 1 / x⁴ + 2( x² * 1 / x² ) = 729

⇒ x⁴ + 1 / x⁴ + 2 = 729

⇒ x⁴ + 1 / x⁴ = 729 - 2

⇒ x⁴ + 1 / x⁴ = 727

Answer 2

$x - \frac{1}{x} = 5 \\ \\ ( {x - \frac{1}{x} })^{2} = 25 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 25 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 27 \\ \\ ( { {x}^{2} + \frac{1}{ {x}^{2} } })^{2} = 729 \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 729 \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } = 727$