Question

Please tell step by step solution ​

Answer 1

Answer:

${\Large\frac{5}{4}}$

Step-by-step explanation:

$\implies$ $(x+{\Large\frac{1}{x}})^2=x^2+{\Large\frac{1}{x^2}}+2$

$\implies$ $(x+{\Large\frac{1}{x}})^2={\Large\frac{17}{4}}+2$

$\implies$ $(x+{\Large\frac{1}{x}})^2={\Large\frac{17+8}{4}}$

$\implies$ $(x+{\Large\frac{1}{x}})=\sqrt{\Large\frac{25}{4}}$

$\implies$ $\boxed{(x+{\frac{1}{x}})={\frac{5}{4}}}$

$\implies$ $(x-{\Large\frac{1}{x}})^2=x^2+{\Large\frac{1}{x^2}}-2$

$\implies$ $(x-{\Large\frac{1}{x}})^2={\Large\frac{17}{4}}-2$

$\implies$ $(x-{\Large\frac{1}{x}})^2={\Large\frac{17-8}{4}}$

$\implies$ $(x-{\Large\frac{1}{x}})=\sqrt{\Large\frac{9}{4}}$

$\implies$ $\boxed{(x-{\frac{1}{x}})={\frac{3}{4}}}$

Now, substitute in the given equation :

$\implies$ ${\Large\frac{2}{5}}(x+{\Large\frac{1}{x}})+(x-{\Large\frac{1}{x}})$

$\implies$ ${\Large\frac{2}{5}}({\Large\frac{5}{4}})+({\Large\frac{3}{4}})$

$\implies$ ${\Large\frac{10}{20}}+{\Large\frac{3}{4}}$

$\implies$ ${\Large\frac{10+15}{20}}$

$\implies$ $\boxed{\Large\frac{5}{4}}$

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Answer 2

Answer:

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