If a²−3b²=117 and a²+b²=153, then what is the value of a+ab?

Answer 1

Solve as a system of equations by solving for a². Use that answer to solve for b by finding the square root. Then you can find a + ab.

a² - 3b² = 117

a² = 3b² +117

substitute the expression for± a²

a² + b² = 153

3b² +117 + b² = 153

4b² + 117 = 153

4b² = 36

b² = 9

b = 3

substitute 9 for b² in the other equation

a² - 3b² = 117

a² - 3(9) = 117

a² - 27 = 117

+27 +27

a² = 144

a = 12

a + ab = 12 + 12(3) = 12 + 36 = 48

*I am making the assumption that your teacher wants only the positive square root. If he/she is wanting the positive and negative square roots, you will have to calculate with a=12, a=-12, b=3, and b=-3. In this case, you will need the next three calculations:

12 + 12 x -3 = 12 + -36 = -24

-12 + -12 x 3 = -12 + -36 = -48

-12 + -12 x -3 = -12 + 36 = 24