Question

Simplify:(x+1∕x)²+(x-1∕x)²​

Answer 1

Answer:

${(x + \frac{1}{x}) }^{2} + {(x - \frac{1}{x}) }^{2} \\ = {x}^{2} + { (\frac{1}{x} )}^{2} + 2 \times x \times \frac{1}{x} + {x}^{2} + { (\frac{1}{x}) }^{2} - 2 \times x \times \frac{1}{x} \\ = 2 {x}^{2} + \frac{2}{ {x}^{2} } \\ = \frac{2 {x}^{4} + 2 }{ {x}^{2} }$

Answer 2

Answer:

solution=x^2+1/x^2+2.x.1/x+(x^2+1/x^2-2.x.1/x)

=x^2+1/x^2+2+x^2+1/x^2-2

=2x^2+2/x^2

=2(x^2+1/x^2) Ans.