Question

find the value of x^2+1/x^2 if x=1/x=√3​

Answer 1

Answer:

1

Step By Step Explanation:

${x} + \frac{1}{x} = √3 \\ (by \: squaring \: both \: the \: sides \:) \\ = {( x + \frac{1}{x}) }^{2} = {√3}^{2} \\( as \: {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2 \times a \times b) \\ = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 3 \\ = {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 3 \\ ={x}^{2} + \frac{1}{ {x}^{2} } = 1$

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