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

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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

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