InterviewSolution
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InterviewSolution
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If `x , y , z`are natural numbers such that `cot^(-1)x+cot^(-1)y=cot^(-1)z`then the number of ordered triplets `(x , y , z)`that satisfy the equation is0 (b) 1(c) 2 (d) Infinite solutions |
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Answer» Correct Answer - D `x = 1, y =1` is not a solution of the given equation. Suppose `(x, y) != (1,1)` Then `((1)/(x) + (1)/(y))/(1-(1)/(xy)) = (1)/(z)` `rArr x(z -y) = -(1 + yz)` `rArr x = -((1 + xyz))/(z -y)` If `y = n + 1, z = n " then " x = n^(2) + n+1` All such numbers are solutions of the given equation |
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