InterviewSolution
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InterviewSolution
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The Value of \({\left( {\frac{{4 + 2\sqrt 3 }}{{4 - 2\sqrt 3 }} + \;\frac{{3 - \sqrt 3 }}{{2 + 2\sqrt 3 }} - \frac{{11}}{2} - 5\sqrt 3 } \right)^{9999}}\) is1). (4 + 2√3)99992). (3 – √3)99993). (√3)99994). None of these |
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Answer» $({\LEFT( {\frac{{4 + 2\sqrt 3 }}{{4 - 2\sqrt 3 }} + \;\frac{{3 - \sqrt 3 }}{{2 + 2\sqrt 3 }} - \frac{{11}}{2} - 5\sqrt 3 } \right)^{9999}})$ $( = {\left( {\left( {\frac{{4 + 2\sqrt 3 }}{{4 - 2\sqrt 3 }} \times \frac{{4 + 2\sqrt 3 }}{{4 + 2\sqrt 3 }}} \right) + \;\left( {\frac{{3 - \sqrt 3 }}{{2 + 2\sqrt 3 }} \times \frac{{2 - 2\sqrt 3 }}{{2 - 2\sqrt 3 }}} \right) - \frac{{11}}{2} - 5\sqrt 3 } \right)^{9999}})$ $( = {\left( {\frac{{16 + 12 + 16\sqrt 3 }}{{16 - 12}} + \frac{{6 - 6\sqrt 3 - 2\sqrt 3 + 6}}{{4 - 12}} - \frac{{11}}{2} - 5\sqrt 3 } \right)^{9999}})$ $( = {\left( {\frac{{28 + 16\sqrt 3 }}{4} + \frac{{12 - 8\sqrt 3 }}{{ - 8}} - \frac{{11}}{2} - 5\sqrt 3 } \right)^{9999}}{\rm{\;}})$ $( = {\left( {\frac{{28 + 16\sqrt 3 }}{4} - \frac{{12 - 8\sqrt 3 }}{8} - \frac{{11}}{2} - 5\sqrt 3 } \right)^{9999}})$ $( = {\left( {\frac{{44 + 40\sqrt 3 }}{8} - \frac{{11}}{2} - 5\sqrt 3 } \right)^{9999}})$ $( = {\left( {\frac{{11}}{2} + 5\sqrt 3 - \frac{{11}}{2} - 5\sqrt 3 } \right)^{9999}})$ = 0 |
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