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Q1. a, b are natural numbers, if 9a^2 = 12a + 96 and b^2 = 2b+3. Then the value of 2018(a+b) is?
Ans. Given that, 9a^2 = 12a +96
9a^2 - 12a = 96
9a^2 - 12a + 4 = 96 + 4
(3a - 2)^2 = 100
3a - 2 = 10
3a = 12
a = 4
and, b^2 = 2b + 3
b^2 - 2b = 3
b^2 - 2b +1 = 3 + 1
(b - 1)^2 = 4
b - 1 = 2
b = 3
Now, 2018(a+b)
= 2018 (4+3)
= 2018 * 7
= 14126
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