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
Please explain
A) 3
B) 9
C) 10
D) 12
E) 14
OA - E
Please explain
Use the special quadratic x² - y² = (x + y)(x - y).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
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.
