If x + \; 1/x = \; 5/2 then what is the value of the following? \; {5x}{7x² - 3x + 7}

Correct Answer is : 1029\; 10/292910

Correct Answer is : 1029\; 10/292910

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UPSC CDS 1 2022 Math Paper

Question : 4 of 100

Marks: +1, -0

x + \; \frac{1}{x} = \; \frac{5}{2}

\; \frac{5x}{7x^{2} - 3x + 7}

Solution: 👈: Video Solution

Given:

x + \; \frac{1}{x} = \; \frac{5}{2} \;\; \cdots(i)

Formula Used:

(a+b)^{2}=a^{2}+b^{2}+2ab

Calculation:

We have to find the value of

\; \frac{5x}{7x^{2} - 3x + 7}

Taking

x

common from the denominator, we get

\; \frac{5x}{x\left(7x-3+\;\frac{7}{x}\right)}

\Rightarrow \; \frac{5}{\left(7x + \;\frac{7}{x} - 3\right)}

\Rightarrow \; \frac{5}{\left(7\left[x + \;\frac{1}{x}\right] - 3\right)}

From (i)

\Rightarrow \; \frac{5}{7 \times \;\frac{5}{2} - 3} = \; \frac{10}{35 - 6}

\Rightarrow \; \frac{10}{29}

\therefore

The required value of the expression is

\; \frac{10}{29}

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