If 2a 2 + b = 10 and C (b/4 + 3a) = 11, what is the positive value of a?

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If 2a 2 + b = 10 and C (b/4 + 3a) = 11, what is the positive value of a?

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Answer: 3

Explanation:

Solve 2 a 2 + b = 10 for b : b = 10 C 2 a 2 .

Substitute (10 C 2 a 2 ) for b in the second equation and solve for a :

C10 + 2 a 2 + 12 a = 44

2 a 2 + 12 a C 54 = 0

2 a C 6 = 0, a = 3

a + 9 = 0, a = C9

The positive value of a is 3.