Question

if x+1/x=5 then find x^2+1/x^2

Answer 1

x + 1/ x = 5
(x+1/x)^2 = 5^2
x^2 + 1/ x ^2 +2*x*1/x = 25
x^2 +1/x^2. = 25 -2
x ^2 + 1/ x^2 = 23

Answer 2

here is your answer,
$x + 1 \div x = 5 \\( x + 1 \div x) {}^{2} = 5 {}^{2} (squaring \: both \: sides) \\ x { }^{2} + 1 \div x {}^{2} + 2 = 25 \\ x {}^{2} + 1 \div x {}^{2} = 25 - 2 \\ x { }^{2} + 1 \div {x}^{2} = 23$