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Identities — MATHS STD 8 — Question

ICSE BoardEnglish MediumSTD 8MATHSIdentities4 Marks
Question
If $2 x-\frac{1}{2 x}=4$, find $: 4 x^2+\frac{1}{4 x^2}$
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Answer

$ 2 \mathrm{x}-\frac{1}{2 \mathrm{x}}=4$
$ \Rightarrow\left(2 \mathrm{x}-\frac{1}{2 \mathrm{x}}\right)^2=(4)^2$
$ \Rightarrow(2 \mathrm{x})^2+\left(\frac{1}{2 \mathrm{x}}\right)^2-2 \times 2 \mathrm{x} \times \frac{1}{2 \mathrm{x}}=16$
$ \Rightarrow 4 \mathrm{x}^2+\frac{1}{4 \mathrm{x}^2}-2=16$
$ \Rightarrow 4 \mathrm{x}^2+\frac{1}{4 \mathrm{x}^2}=16+2$
$ \Rightarrow 4 \mathrm{x}^2+\frac{1}{4 \mathrm{x}^2}=18$

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