The value of \(\frac{\sqrt{5}+\sqrt{3}}{\sqrt{8-2 \sqrt{15}}}+\frac{\sqrt{11+2 \sqrt{30}}}{\sqrt{6}-\sqrt{5}}\) is
Question and options
The value of is
Answer and explanation
Correct answer: D - \(15+\sqrt{15}+2 \sqrt{30}\)
sqrt(8-2sqrt15) = sqrt5 - sqrt3, so the first term = (sqrt5+sqrt3)^2/2 = 4 + sqrt15. sqrt(11+2sqrt30) = sqrt6 + sqrt5, so the second term = (sqrt6+sqrt5)^2/(6-5) = 11 + 2sqrt30. Sum = 15 + sqrt15 + 2sqrt30.
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