If x-1 x =15 4 , than (x+1 x )= - Vidyadip

Question

If $\text{x}-\frac{1}{\text{x}}=\frac{15}{4},$ than $\Big(\text{x}+\frac{1}{\text{x}}\Big)=$

✓

Answer

$\frac{17}{4}$
Solution:
$\Rightarrow\text{x}+\frac{1}{\text{x}}=\frac{15}{4}$
Now, $\Big(\text{x}-\frac{1}{\text{x}}\Big)^2=\Big(\frac{15}{4}\Big)^2$
$\Rightarrow(\text{x}^2)+\Big(\frac{1}{\text{x}^2}\Big)-2\times\text{x}\times\frac{1}{\text{x}}=\frac{225}{16}$
$\Rightarrow(\text{x}^2)+\Big(\frac{1}{\text{x}^2}\Big)=\frac{225}{16}+2$
$\Rightarrow(\text{x})^2+\Big(\frac{1}{\text{x}^2}\Big)=\frac{257}{16}$
$\Rightarrow(\text{x}^2)+\Big(\frac{1}{\text{x}^2}\Big)+2\times\text{x}\times\frac{257}{16}+2\times\text{x}\times\frac{1}{\text{x}}\\=\frac{257}{16}+2\times\text{x}\times\frac{1}{\text{x}}$
$\Rightarrow\Big(\text{x}+\frac{1}{\text{x}}\Big)^2=\frac{257+32}{16}=\frac{289}{16}$
$\Rightarrow\Big(\text{x}+\frac{1}{\text{x}}\Big)=\sqrt{\frac{289}{16}}=\frac{17}{4}$

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