Question

If 3 p - 2 q equal to 10 and pq equal to -1 then find the value of 9 p square + 4 q square

Answer 1

If 3p - 2q = 10 and pq = -1, then find the value of 9p^2 + 4q^2

Solution -

$3p - 2q \: = 10$

${(3p - 2q)}^{2} = {10}^{2}$

As we know, (a-b)^2 = a^2 + b^2 - 2ab

${(3p)}^{2} \: + {(2q)}^{2} + 2 \times 3p \times 2q \: =$

${9p }^{2} + {4q}^{2} - 12pq$

As we know, pq = -1

${9p}^{2} + {4q}^{2} - 12 \times ( - 1)$

${9p}^{2} + {4q}^{2} + 12 \: = 100$

${9p}^{2} + {4q}^{2} = 100 - 12$

${9p}^{2} + {4q}^{2} = 88$

Answer = 9p^2 +4q^2 = 88 ......

Hope it helps u .....