1.

If =a 2+√3 then find the Value of a2 +1/a2​

Answer» <html><body><h3><u>EXPLANATION</u>.</h3><p>⇒ a = <a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a> + √<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>.</p><p>As we know that,</p><p></p><p>We can write equation as,</p><p>⇒ 1/a = 1/(2 + √3).</p><p></p><p>Now, <a href="https://interviewquestions.tuteehub.com/tag/rationalize-619536" style="font-weight:bold;" target="_blank" title="Click to know more about RATIONALIZE">RATIONALIZE</a> the equation, we get.</p><p>⇒ 1/a = 1/(2 + √3) x (2 - √3)/(2 - √3).</p><p>⇒ 1/a = (2 - √3)/[(2)² - (√3)²].</p><p>⇒ 1/a = (2 - √3)/[4 - 3].</p><p>⇒ 1/a = (2 - √3)/1 = 2 - √3.</p><p></p><p><strong><u>To find :</u></strong></p><p>⇒ <strong><u>a² + 1/a²</u></strong>.</p><p></p><p>⇒ a² = (2 + √3)².</p><p>⇒ a² = 4 + 3 + 4√3.</p><p>⇒ a² = <a href="https://interviewquestions.tuteehub.com/tag/7-332378" style="font-weight:bold;" target="_blank" title="Click to know more about 7">7</a> + 4√3.</p><p></p><p>⇒ 1/a² = (2 - √3)².</p><p>⇒ 1/a² = 4 + 3 - 4√3.</p><p>⇒ 1/a² = 7 - 4√3.</p><p></p><p>⇒ (a² + 1/a²) = [(7 + 4√3) + (7 - 4√3].</p><p>⇒ (a² + 1/a²) = [7 + 4√3 + 7 - 4√3].</p><p>⇒ <strong><u>(a² + 1/a²) = 14</u></strong>.</p></body></html>


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