if 3a+4b =16 and ab =4 , find the value of 9a + 16b
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Answer: Given: 3a+4b = 16 ... (i) and ab = 4 ... (ii)
Squaring (i), we get
(3a+4b)2 = 162
9a2 + 16b2 + 24ab = 256
9a2 + 16b2 + 24 x 4 = 256 ... Using (ii)
9a2 + 16b2 = 256 - 96 = 160
Hence, 9a2 + 16b2 = 160.
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