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Algebraic Identities — Maths STD 9 — Question

CBSE BoardEnglish MediumSTD 9MathsAlgebraic Identities1 Mark
MCQ
If $\frac{a}{b}+\frac{b}{a}=2$, then $\left(\frac{a}{b}\right)^{10}-\left(\frac{b}{a}\right)^{10}$ is equal to
  • A
    $\frac{2^{10}-1}{2^{10}}$
  • B
    2
  • ✓
    $0$
  • D
    $\frac{2^{20}+1}{2^{10}}$
✓

Answer

Correct option: C.
$0$
(c)
We have, $\frac{a}{b}+\frac{b}{a}=2$
$\Rightarrow \quad\left(\sqrt{\frac{a}{b}}\right)^2+\left(\sqrt{\frac{b}{a}}\right)^2-2 \sqrt{\frac{a}{b}} \times \sqrt{\frac{b}{a}}=0$
$\Rightarrow \quad\left(\sqrt{\frac{a}{b}}-\sqrt{\frac{b}{a}}\right)^2=0 \Rightarrow \sqrt{\frac{a}{b}}=\sqrt{\frac{b}{a}} \Rightarrow \frac{a}{b}=\frac{b}{a} \Rightarrow\left(\frac{a}{b}\right)^{10}=\left(\frac{b}{a}\right)^{10} \Rightarrow\left(\frac{a}{b}\right)^{10}-\left(\frac{b}{a}\right)^{10}=0$.

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