SAT Math Multiple Choice Practice Question 449: Answer and Explanation
11. If (a + b)2 = 49, and ab = 10, which of the following represents the value of b in terms of a ?
Correct Answer: B
B One way to solve this problem is to Plug In. First, simplify (a + b)2 = 49 by taking the square root of both sides to find a + b = 7. Now, brainstorm some values for a and b that make a + b = 7 and ab = 10. Let's say a is 2 and b is 5. So, find the answer that yields 5 when you plug in a = 2. Only B works. The second, more complicated, way is to FOIL out (a + b)2 = 49 to get a2 + 2ab + b2 = 49. Plug in 10 for ab to get a2 + 2(10) + b2 = 49. That means, a2 + 20 + b2 = 49. Subtract 20 from both sides to get a2 + b2 = 29. Subtract a2 from both sides to get b2 = 29 – a2. Take the square root of both sides to find b = .