ISEE Mathematics Achievement Question 16: Answer and Explanation

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Question: 16

2. If x2 + y2 = 65 and xy = 28, what is the value of (x + y)2?

  • A. 37
  • B. 93
  • C. 121
  • D. 784

Correct Answer: C

Explanation:

C

The common quadratic (x + y)2 can be written as x2 + 2xy + y2. Rearrange the expression to x2 + y2 + 2xy and substitute in the given values: 65 + 2(28) = 65 + 56 + 121.

You can guess and check to find numbers that work. If xy = 28, then x and y can be 1 and 28, 2 and 14, or 4 and 7. Testing these in x2 + y2 shows that 4 and 7 work. Therefore, (x + y)2 = (4 + 7)2 = 121.

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