Question

Answer the question attached.

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Answer 1

$\huge \fbox \pink{Answer:}$

• There are two ways to answer the question you asked.

$\sf \colorbox{pink} {First way}$

$\textbf{Given:}$

$\frac{1}{ \sqrt{3} + \sqrt{2} } - \frac{2}{ \sqrt{5} - \sqrt{3} } - \frac{3}{ \sqrt{2} - \sqrt{5} }$

$\fbox{Solve}$

$= \frac{1 \times \sqrt{3} - \sqrt{2} }{( \sqrt{3 + \sqrt{2} })( \sqrt{3} - \sqrt{2} ) } - \frac{2( \sqrt{5} + \sqrt{3} )}{( \sqrt{5} - \sqrt{3})( \sqrt{5} + \sqrt{3} ) } - \frac{3( \sqrt{2} + \sqrt{5} )}{( \sqrt{2} - \sqrt{5} )( \sqrt{2} + \sqrt{5} )}$

$= \frac{ \sqrt{3} - \sqrt{2} }{( \sqrt{3} {)}^{2} - ( \sqrt{2} {)}^{2} } - \frac{2( \sqrt{5} + \sqrt{3}) }{( \sqrt{5} {)}^{2} - ( \sqrt{3} {)}^{2} } - \frac{3( \sqrt{2} + \sqrt{5} ) }{( \sqrt{2} {)}^{2} - ( \sqrt{5} {)}^{2} }$

$[∴(a + b)(a - b) = {a}^{2} - {b}^{2} ]$

$= \frac{ \sqrt{3} - \sqrt{2} }{3 - 2} - \frac{2( \sqrt{5} + \sqrt{3}) }{5 - 3} - \frac{3( \sqrt{2} + \sqrt{5}) }{2 - 5}$

$= \frac{ \sqrt{3} - \sqrt{2} }{1} - \frac{2( \sqrt{5} + \sqrt{3} )}{2} - \frac{3( \sqrt{2} + \sqrt{5} )}{ - 3}$

$⇒ \sqrt{3} - \sqrt{2} - \sqrt{5} - \sqrt{3} + \sqrt{2} + \sqrt{5} = 0$

$\textbf{:Hence} \frac{1}{ \sqrt{3} + \sqrt{2} } - \frac{2}{ \sqrt{5} - \sqrt{3} } - \frac{3}{ \sqrt{2} - \sqrt{5} } = 0$

$\sf \colorbox{pink} {Second way}$

$\text{The second method is in the pic above}$

$\\ \\ \\ \\ \\ \sf \colorbox{gold} {\red(ANSWER ᵇʸ ⁿᵃʷᵃᵇ⁰⁰⁰⁸}$

Answer 2

Answer:

Hope it helps you...

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