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If x = 1 + √6 + √7, then the value of \(\left( {x + \frac{1}{{x - 1}}} \right)\) is1). 1 + 2√72). 6 + √73). 1 + 2√64). 2√7 – 1 |
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Answer» x = 1 + √6 + √7 $(\BEGIN{ARRAY}{l}x + \FRAC{1}{{x - 1}}\\ = \left( {1 + \sqrt 6+ \sqrt 7 } \right) + \frac{1}{{1 + \sqrt 6+ \sqrt 7- 1}}\\ = 1 + \sqrt 6+ \sqrt 7+ \frac{1}{{\sqrt 6+ \sqrt 7 }} \TIMES \frac{{\sqrt 6- \sqrt 7 }}{{\sqrt 6- \sqrt 7 }}\;\\ = 1 + \sqrt 6+ \sqrt 7+ \frac{{\left( {\sqrt 6- \sqrt 7 } \right)}}{{6 - 7}}\end{array})$ = 1 + √6 + √7 + √7 – √6 = 1 + 2√7 |
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