Question

solve this..........................​

Answer 1

Answer : 35

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Solution :

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Given that :

$3x + \frac{2}{x} = 7$

As we know that :

(a-b)² = (a+b)² - 4ab

$= > {(3x - \frac{2}{x} )}^{2} = {(3x + \frac{2}{x} )}^{2} - 4(3x)( \frac{2}{x} ) \\ \\ = > {(3x + \frac{2}{x} )}^{2} = {7}^{2} - 24 \\ \\ = > {(3x + \frac{2}{x} )}^{2} = 49 - 24 = 25 \\ \\ = > (3x - \frac{2}{x} ) = 5$

Now, we have to find the value of :

$9 {x}^{2} - \frac{4}{ {x}^{2} }$

As we know that :

a²-b² = (a+b)(a-b)

$= > 9 {x}^{2} - \frac{4}{ {x}^{2} } = {(3x)}^{2} - { (\frac{2}{x}) }^{2} \\ \\ = > 9{x}^{2} - \frac{4}{ {x}^{2} } = (3x + \frac{2}{x} )(3x - \frac{2}{x} ) \\ \\ = > 9 {x}^{2} - \frac{4}{ {x}^{2} } = 7 \times 5 \\ \\ = > 9{x}^{2} - \frac{4}{ {x}^{2} } = 35$