if (4a75b) = 16 and ab=4 find the value of 16a2+25b2
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Given: (3a+4b)=16 ... (i) and ab = 4 ... (ii)
Squaring (i), we get
(3a+4b)2 = 162
9a2 + 16b2 + 2 x 3a x 4b = 256
9a2 + 16b2 + 24ab = 256
9a2 + 16b2 = 256 - 24ab
9a2 + 16b2 = 256 - 24(4) ... Using (ii)
9a2 + 16b2 = 256 - 96
9a2 + 16b2 = 160
Hence, the value of 9a2 + 16b2 is 160.
Step-by-step explanation:
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