If x/y + y/x = 2, then what is the value of { (x² + y²) / (xy + y²) } ?
2024
If x/y + y/x = 2, then what is the value of { (x² + y²) / (xy + y²) } ?
Answer: C. 1 — Given: x/y + y/x = 2. Step 1: Multiply both sides by xy to eliminate denominators: x² + y² = 2xy. Step 2: Rearranging gives x² - 2xy + y² = 0, which…
- A.
0
- B.
1/4
- C.
1
- D.
More than one of the above
- E.
None of the above
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Correct answer: C
Given: x/y + y/x = 2.
Step 1: Multiply both sides by xy to eliminate denominators: x² + y² = 2xy.
Step 2: Rearranging gives x² - 2xy + y² = 0, which simplifies to (x - y)² = 0. Therefore, x = y.
Step 3: Substitute x = y into the expression (x² + y²)/(xy + y²):
(x² + x²)/(x·x + x²) = (2x²)/(x² + x²) = 2x²/2x² = 1.
Thus, the value of the expression is 1.
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