Question

if x +1/x=5, find the values of
a. x^2+1/x^2
b. x^4+1/4^4​

Answer 1

Answer:

$x + \frac{1}{x} = 5 \\ \: squaring \: both \: side \\ (x + \frac{1}{x} ) ^{2} = 25 \\ x {}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 25 \\ x {}^{2} + \frac{1}{x {}^{2} } + 2 = 25 \\ x {}^{2} + \frac{1}{x {}^{2} } = 25 - 2 = 23 \\ \\ \: now \ \: again \: squaring \: both \: side \\ (x {}^{2} + \frac{1}{x {}^{2} } ) {}^{2} = (23) {}^{2} \\ x {}^{4} + \frac{1}{x {}^{4} } + 2 \times x {}^{2} \times \frac{1}{ {x}^{2} } = 529 \\ x {}^{4} + \frac{1}{ {x}^{4} } = 529 - 2 = 527$

Answer 2

Hey There!
Here's your answer!

Hope it's helpful!
-medhani