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Question
If p and q are the roots of the equation lx2 + nx + n = 0, show that `sqrt("p"/"q") + sqrt("q"/"p") + sqrt("n"/l)` = 0
Solution
p and q are the roots of the equation lx2 + nx + n = 0
p + q = `- "n"/l`
pq = `"n"/l`
L.H.S
`sqrt("p"/"q") + sqrt("q"/"p") + sqrt("n"/l) = sqrt("p")/sqrt("q") + sqrt("q")/sqrt("p") + sqrt("n")/sqrt(l)`
= `("p" + "q")/(sqrt("p") sqrt("q")) + sqrt("n")/(sqrt(l)`
= `(- "n"/6)/sqrt("pq") + sqrt("n")/sqrt(l)`
= `(- "n"/l)/(sqrt("n")/sqrt(l)) + sqrt("n")/sqrt(l)`
= `(- "n"/l + "n"/l)/sqrt("n"/l)`
= 0
= R.H.S
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