# SAT Math Multiple Choice Practice Question 449: Answer and Explanation

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**Question: 449**

**11.** If (*a* + *b*)^{2} = 49, and *ab* = 10, which of the following represents the value of *b* in terms of *a* ?

A.

B.

C.

D.

E.

**Correct Answer:** B

**Explanation:**

**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 *a*^{2} + 2*ab* + *b*^{2} = 49. Plug in 10 for *ab* to get *a*^{2} + 2(10) + *b*^{2} = 49. That means, *a*^{2} + 20 + *b*^{2} = 49. Subtract 20 from both sides to get *a*^{2} + *b*^{2} = 29. Subtract *a*^{2} from both sides to get *b*^{2} = 29 – *a*^{2}. Take the square root of both sides to find *b* = .