Question

Solving equations (algebra). Thank you!

Answer 1

Answer:

$\large\boxed{\dfrac{1}{x^2}+x^2=23}$

Step-by-step explanation:

$\left(\dfrac{1}{x}+x\right)^2=25\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\\left(\dfrac{1}{x}\right)^2+2(x\!\!\!\!\diagup)\left(\dfrac{1}{x\!\!\!\!\diagup}\right)+x^2=25\\\\\dfrac{1}{x^2}+2+x^2=25\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{x^2}+x^2=23$