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If a and b are rational numbers, find their value if :3 √5+ √3/√5− √3 = a + b√15

Answer» <html><body><p><strong>Answer:</strong></p><p><a href="https://interviewquestions.tuteehub.com/tag/mark-555248" style="font-weight:bold;" target="_blank" title="Click to know more about MARK">MARK</a> me as brainlist</p><p><strong>Step-by-step explanation:</strong></p><p>It is given that </p><p><a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a></p><p></p><p> − </p><p>3</p><p></p><p> </p><p>5</p><p></p><p> + </p><p>3</p><p></p><p> </p><p></p><p> =a+b </p><p><a href="https://interviewquestions.tuteehub.com/tag/15-274069" style="font-weight:bold;" target="_blank" title="Click to know more about 15">15</a></p><p></p><p> </p><p></p><p><a href="https://interviewquestions.tuteehub.com/tag/simplify-644378" style="font-weight:bold;" target="_blank" title="Click to know more about SIMPLIFY">SIMPLIFY</a> the term on the L.H.S. by rationalizing,</p><p></p><p>5</p><p></p><p> − </p><p>3</p><p></p><p> </p><p>5</p><p></p><p> + </p><p>3</p><p></p><p> </p><p></p><p> × </p><p>5</p><p></p><p> + </p><p>3</p><p></p><p> </p><p>5</p><p></p><p> + </p><p>3</p><p></p><p> </p><p></p><p> </p><p></p><p>= </p><p>( </p><p>5</p><p></p><p> ) </p><p>2</p><p> −( </p><p>3</p><p></p><p> ) </p><p>2</p><p> </p><p>( </p><p>5</p><p></p><p> + </p><p>3</p><p></p><p> ) </p><p>2</p><p> </p><p></p><p> </p><p></p><p>= </p><p>5−3</p><p>( </p><p>5</p><p></p><p> ) </p><p>2</p><p> +( </p><p>3</p><p></p><p> ) </p><p>2</p><p> +2 </p><p>5</p><p></p><p> </p><p>3</p><p></p><p> </p><p></p><p> </p><p></p><p>= </p><p>2</p><p>5+3+2 </p><p>15</p><p></p><p> </p><p></p><p> </p><p></p><p>= </p><p>2</p><p>8+2 </p><p>15</p><p></p><p> </p><p></p><p> </p><p></p><p>=4+ </p><p>15</p><p></p><p> </p><p></p><p>Now,</p><p>4+ </p><p>15</p><p></p><p> =a+b </p><p>15</p><p></p><p> </p><p></p><p>⇒a=4 and b=1</p></body></html>


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