Operation # is defined as: a # b = 4a² + 4b² + 8ab for all non-negative integers. What is the value of (a + b) + 3, when a # b = 100? A. 5 B. 8 C. 10 D. 13 E. 17
(B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So 4a² + 4b² + 8ab = 100
We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore (2a + 2b)² = 100. (2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10.
(a + b) + 3 = 10/2 + 3 = 8.
The correct answer is B. ---------- The only question I have about this problem is the transition from (2a + 2b)² = 100 to 2(a + b) = 10. Obviously the square root was taken but only of the (a + b)?
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