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यदि `x=(4sqrt(15))/(sqrt(5)+sqrt(3))` है तो `(x+sqrt(20))/(x-sqrt(20))+(x+sqrt(12))/(x-sqrt(12))` का मान ज्ञात करें।A. 1B. 2C. `sqrt(3)`D. `sqrt(5)` |
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Answer» Correct Answer - B `x=(4sqrt(15))/(sqrt(5)+sqrt(3))` `(x+sqrt(20))/(x-sqrt(20))+(x+sqrt(12))/(x-sqrt(12))=?` `:. x=(4xxsqrt(5)xxsqrt(3))/(sqrt(5)+sqrt(3))=(2xx(sqrt(5)xxsqrt(12)))/(sqrt(15)+sqrt(3))` or `(2xxsqrt(20)xxsqrt(3))/(sqrt(5)+sqrt(3))` `x/(sqrt(12))=(2sqrt(5))/(sqrt(5)+sqrt(3))` by C-D rule `(x+sqrt(12))/(x-sqrt(12))=(2sqrt(5)+sqrt(5)+sqrt(3))/(2sqrt(5)-sqrt(5)-sqrt(3))` `=(3sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))` `x/(sqrt(20))=(2sqrt(3))/(sqrt(5)+sqrt(3))` `(x+sqrt(20))/(x-sqrt(20))=(2sqrt(3)+sqrt(5)+sqrt(3))/(2sqrt(3)-sqrt(5)-sqrt(3))` `=(3sqrt(3)+sqrt(5))/(sqrt(3)-sqrt(5))` `:. (x+sqrt(12))/(x-sqrt(12))+(x+sqrt(20))/(x-sqrt(20))` `=(3sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(3sqrt(3)+sqrt(5))/(sqrt(3)-sqrt(5))` `= (3sqrt(5)+sqrt(3)-3sqrt(3)-sqrt(5))/(sqrt(5)-sqrt(3))` `=(2sqrt(5)-2sqrt(3))/(sqrt(5)-sqrt(3))=2` |
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