Question

3p-2q=10,pq=-1 find 9p^2+4q^2
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Answer 1

use ( a-b) ^2

(3p-2q) ^2 =10^2=100

3p^2 +2q^2- 12pq =100

9p^2 + 4q^2 =100+ 12pq = 100 -12 =88

answer 88

Answer 2

The value of $9p^2+4q^2$ = 88

Step-by-step explanation:

Given,

3p - 2q = 10 and pq = - 1

To find, the value of $9p^2+4q^2=?$

∴ 3p - 2q = 10

Using the algebraic identity,

$( a-b)^2=a^{2} +b^{2} -2ab$

∴ 3p - 2q = 10

⇒ $(3p-2q) ^2 =10^2$

⇒ $(3p)^2 +(2q)^2- 2(3p)(2q) =100$

⇒ $9p^2 +4q^2- 12pq =100$

Put 3p - 2q = 10, pq = - 1, we get

⇒ $9p^2 + 4q^2-12(-1)=100$

⇒ $9p^2 + 4q^2+12=100$

⇒ $9p^2 + 4q^2=100-12=88$

∴ The value of $9p^2+4q^2$ = 88