InterviewSolution
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InterviewSolution
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if `c!=0` and the equation `p/(2x)=a/(x+c)+b/(x-c)` has two equal roots, then p can beA. `(sqrt(a) - sqrt(b))^(2) `B. `(sqrt(a)+ sqrt(b))^(2) `C. a+ bD. a - b |
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Answer» Correct Answer - 1.2 We can write the given equation as ` (p)/(2x) = ((a + b) x + c(b - a))/(x^(2) - c^(2))` or ` p(x^(2) - c^(2)) = 2 (a + b) x^(2) - 2 c (a - b) x ` or `(2a + 2b - p )x^(2) - 2c (a - b) x + pc^(2) = 0` for this equation to have equal roots, `c^(2) (a - b)^(2) - pc^(2) (2a + 2b - p) = 0 ` or ` (a - b)^(2) - 2p (a + b) + p^(2) = 0 [ because c^(2) ne 0 ]` or `[ p - (a + b)]^(2) = (a + b)^(2) - (a - b)^(2) = 4ab` or ` p - (a + b) = pm 2 sqrt(ab)` or `p = a + b pm 2 sqrt(ab) = (sqrt(a ) pm sqrt(b))^(2)` . |
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