Question

x+1/x=3,find x^2+1/x^2​

Answer 1

Answer:

Using the formula:-(a+b)^2

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

=>(3)^2=x^2+1/x^2+2

=>9=x^2+1/x^2+2

=>x^2+1/x^2=9-2=7 [ANS]

Answer 2

$\frac{x + 1}{x} = 3 \\ \\ x + 1 = 3x \\ 3x - x = 1 \\ 2x = 1 \\ x = \frac{1}{2}$

$\frac{ {x}^{2} + 1 }{ {x}^{2} } \\ \\ = \frac{ {( \frac{1}{2}) }^{2} + 1}{( { \frac{1}{2}) }^{2} } \\ \\ = \frac{ \frac{1}{4} + 1}{ \frac{1}{4} } \\ \\ = \frac{ \frac{5}{4} }{ \frac{1}{4} } \\ \\ = \frac{5}{1} \\ = 5$