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Algebraic Identities — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsAlgebraic Identities1 Mark
MCQ
If $\text{x}+\frac{1}{\text{x}}=2,$ then $\text{x}^3+\frac{1}{\text{x}^3}=$
  • A
    $64$
  • B
    $14$
  • C
    $8$
  • ✓
    $2$
✓

Answer

Correct option: D.
$2$
By using identity,
$(a + b)^3 = a^3 + b^3 + 3ab(a + b)$
$\Big(\text{x}+\frac{1}{\text{x}}\Big)^3=\text{x}^3+\frac{1}{\text{x}^3}+3(\not\text{x})\frac{1}{\not\text{x}}\Big(\text{x}+\frac{1}{\text{x}}\Big)\\=\text{x}^3+\frac{1}{\text{x}^3}+3\Big(\text{x}+\frac{1}{\text{x}}\Big)$
Now $\text{x}+\frac{1}{\text{x}}=2$
$\Rightarrow(2)^3=\text{x}^3+\frac{1}{\text{x}^3}+3(2)$
$\Rightarrow\text{x}^3+\frac{1}{\text{x}^3}=(2)^3-3\times2=8-6=2$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}=23$
Hence, correct option is $(d).$

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