InterviewSolution
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InterviewSolution
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If \((x-\frac{1}{x})=4,\) find the value of(i) \((x^2+\frac{1}{x^2}),\)(ii) \((x^4+\frac{1}{x^4}),\) |
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Answer» (i) \(\text{x}-\frac{1}{\text{x}}=4\) Squaring both the sides, \((\text{x}-\frac{1}{\text{x}})^2=4^2\) Using the identity, (a – b)2 = a2 - 2ab + b2 \(\text{x}^2-2+\frac{1}{\text{x}^{2}}=4^2\) \(\Rightarrow \text{x}^2+\frac{1}{\text{x}^{2}}=16+2=18\) -----------(1) (ii) Squaring equation (1) using the identities, (a + b)2 = a2 + 2ab + b2 \(\Rightarrow\text{x}^4+2+\frac{1}{\text{x}^{4}}=324\) \(\Rightarrow \text{x}^4+\frac{1}{\text{x}^4}=324-2=322\) |
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