Question

If 15(2p2 - q2) = 7pq where p and q are positive, then p:q will be?

Answer 1

This is my answer

Thanks

Answer 2

$Given \: 15(2p^{2} - q^{2}) = 7pq$

$\implies 30p^{2} - 15q^{2} - 7pq = 0$

$\implies 30p^{2} - 7pq - 15q^{2} = 0$

/* Splitting the middle term ,we get */

$\implies 30p^{2} - 25pq + 18pq - 15q^{2} = 0$

$\implies 5p( 6p - 5q ) +3q(6p-5q) = 0$

$\implies (6p-5q)(5p+3q) = 0$

$\implies 6p-5q = 0 \: Or \: 5p+3q= 0$

$\implies 6p= 5q \: Or \: 5p = -3q$

$\implies \frac{p}{q}= \frac{5}{6} \: Or \: \frac{p}{q} = \frac{-3}{5}$

/* But p and q are positive */

$Value \: of \: \frac{p}{q}= \frac{5}{6}$

Therefore.,

$\red { Value \:of \: \frac{p}{q}}\green {= \frac{5}{6} }$

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