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If `x, y, z` are distinct positive real numbers is A.P. then `(1)/(sqrt(x)+sqrt(y)), (1)/(sqrt(z)+sqrt(x)), (1)/(sqrt(y)+sqrt(z))` are inA. `A.P.`B. `G.P.`C. `H.P.`D. `A.G.P.` |
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Answer» Correct Answer - A If `x, y, z` are …………. `x, y, z` are in `AP , y - x = z - y` `(sqrt(y)+sqrt(x))(sqrt(y)-sqrt(x))=(sqrt(z)+sqrt(y))` `(sqrt(z)-sqrt(y))` `(sqrt(y)-sqrt(x))/(sqrt(y)+sqrt(z)) = (sqrt(z)-sqrt(y))/(sqrt(y)+sqrt(x))` `((sqrt(y)+sqrt(z))-(sqrt(z)+sqrt(x)))/(sqrt(y)+sqrt(z))` `= ((sqrt(z)+sqrt(x))-(sqrt(x)+sqrt(y)))/((sqrt(x)+sqrt(y)))` `1- (sqrt(z)+sqrt(x))/(sqrt(y)+sqrt(z)) = (sqrt(z)+sqrt(x))/(sqrt(x)+sqrt(y)) - 1` `2 = (sqrt(z)+sqrt(x)) ((1)/(sqrt(x)+sqrt(y))+(1)/(sqrt(y)+sqrt(z)))` `(2)/(sqrt(z)+sqrt(x)) = (1)/(sqrt(x)+sqrt(y)) + (1)/(sqrt(y)+sqrt(z))` `:.` Number are in `A.P` |
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