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If p , q, n , l > 0 and the ratio of the roots of equation : lX^2 + nx + n = 0 be p:q then proove that p/q^1/2 + q /p^1/2 – n/l^1/2 = 0

If p , q, n , l > 0 and the ratio of the roots of equation :     lX^2 + nx + n = 0 be p:q then proove that p/q^1/2 + q /p^1/2 – n/l^1/2 = 0

Grade:11

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
the ratio is p : q
so let roots bept and qt.
so pt + qt = - n/l => p + q = - n/(lt)
and pqt^2 = n/l => pq = n/(lt^2)
now (p/q)^1/2 + (q/p)1/^2 = (p + q)/(pq)^(1/2) = -(n/lt)/((n/l)^1(1/2)t) = - (n/l)^(1/2)
or (p/q)^1/2 + (q/p)1/^2 + (n/l)^(1/2) = 0

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