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Linear Equations — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsLinear Equations2 Marks
Question
If $\Big(\text{x}-\frac{1}{\text{x}}\Big)=4$ find the value of:
$\Big(\text{x}^4+\frac{1}{\text{x}^4}\Big)$
✓

Answer

From the first part:
$\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)=18$
Squaring both the sides:
$\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)^2=18^2$
$\Rightarrow(​​\text{x}^2)^2+2\times(\text{x}^2)\times\Big(\frac{1}{\text{x}^2}\Big)+\Big(\frac{1}{\text{x}^2}\Big)^2=324$
$\Rightarrow\text{x}^4+2+\frac{1}{\text{x}^4}=324$
$\Rightarrow\text{x}^4+\frac{1}{\text{x}^4}=324-2$
$\therefore\text{x}^4+\frac{1}{\text{x}^4}=322$

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