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Factorisation — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSFactorisation2 Marks
Question
Factorise$: x^2+\frac{1}{x^2}-11$
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Answer

$ x^2+\frac{1}{x^2}-11$
$ =x^2+\frac{1}{x^2}-2-9$
$ =x^2+\frac{1}{x^2}-2 \times x \times \frac{1}{x}-9$
$ =\left(x-\frac{1}{x}\right)^2-(3)^2$
$ =\left(x-\frac{1}{x}+3\right)\left(x-\frac{1}{x}-3\right)$

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