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Algebraic Expressions, Identities and Factorisation — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSAlgebraic Expressions, Identities and Factorisation2 Marks
Question
If $\text{x}-\frac{1}{\text{x}}=7$ then find the value of $\text{x}^2+\frac{1}{\text{x}^2}$.
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Answer

Given,$\text{x}-\frac{1}{\text{x}}=7$
Since,$\Big(\text{x}-\frac{1}{\text{x}}\Big)^2=\text{x}^2+\frac{1}{\text{x}^2}-2.\text{x}.\frac{1}{\text{x}}$
$7^2=\text{x}^2+\frac{1}{\text{x}^2}-2$
$\text{x}^2+\frac{1}{\text{x}^2}=49+2$
$\text{x}^2+\frac{1}{\text{x}^2}=51$

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