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InterviewSolution
| 1. |
Find the value of root x-1/root x if x= 2+root 3 |
| Answer» <html><body><h2><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> : </h2><p>√x - 1/√x = √6 </p><p></p><h2><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> : </h2><p>Given : x = 2 + √3 </p><p>To <a href="https://interviewquestions.tuteehub.com/tag/find-11616" style="font-weight:bold;" target="_blank" title="Click to know more about FIND">FIND</a> : √x - 1/√x = ? </p><p></p><p>We have , x = 2 + √3 </p><p></p><p>Thus , </p><p>=> 1/x = 1/(2 + √3)</p><p>=> 1/x = (2 - √3) / (2 + √3)•(2 - √3)</p><p>=> 1/x = (2 - √3) / [ 2² - (√3)² ] </p><p>=> 1/x = (2 - √3) / (4 - 3) </p><p>=> 1/x = (2 - √3) / 1</p><p>=> 1/x = 2 - √3 </p><p></p><p>Now , </p><p>=> (√x - 1/√x)² = (√x)² - 2•√x•(1/√x)+(1/√x)²</p><p>=> (√x - 1/√x)² = x + 2 + 1/x</p><p>=> (√x - 1/√x)² = 2 + √3 + 2 + 2 - √3 </p><p>=> (√x - 1/√x)² = 6 </p><p>=> (√x - 1/√x) = √6 </p><p></p><h3>Hence , </h3><h2>√x - 1/√x = √6</h2></body></html> | |