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Algebra - Special Quadratics

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by MartyMurray » Thu Dec 31, 2015 5:46 am
duahsolo wrote:If 3a - 2b - 2c = 32 and √(3a) - √(2b + 2c) = 4, what is the value of a + b + c?

A) 3
B) 9
C) 10
D) 12
E) 14

OA - E
Use the special quadratic x² - y² = (x + y)(x - y).

3a - 2b - 2c = 3a - (2b + 2c) = (√(3a) + √(2b + 2c))(√(3a) - √(2b + 2c))

So (3a - 2b - 2c)/(√(3a) - √(2b + 2c)) = 32/4 = 8 = (√(3a) + √(2b + 2c))

Add the two terms (√(3a) + √(2b + 2c)) + (√(3a) - √(2b + 2c)) = 2√(3a) = 8 + 4 = 12

√(3a) = 6 3a = 36 a = 12

36 - 2b - 2c = 32

4 = 2b + 2c 2 = b + c

a + b + c = 12 + 2 = 14

The correct answer is E.
Marty Murray
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