Question

if 3a + 2b = 23 and ab = 20 , find 9a^2 + 4b^ 2 (using identities)​

Answer 1

Given :- 3a + 2b = 23 and ab = 20

To find :- 9a^2 + 4b^2

Solution :- Using identity , (A+B)^2 = A^2 + B^2 + 2AB

3a + 2b = 23 (given)

Squaring on both sides,

==> (3a + 2b)^2 = 23^2

==> 9a^2 + 4b^2 + 2 * 3a * 2b = 529

==> 9a^2 + 4b^2 + 12ab = 529

==> 9a^2 + 4b^2 = 529 - 12ab

==> 9a^2 + 4b^2 = 529 - 12 x 20 (given, ab = 20)

==> 9a^2 + 4b^2 = 529 - 240

Therefore, the value of the expression 9a^2 + 4b^2 = 289