Question

If $x + y = 10$ and $xy = 21$, what is the value of $x^2 + y^2$?

• A. 58
• B. 60
• C. 62
• D. 64

Hint:

Use the identity $x^2 + y^2 = (x + y)^2 - 2xy$ for quick computation when sum and product are given.

Answer 1

The Correct Option is A

- Step 1: Use the identity $x^2 + y^2 = (x + y)^2 - 2xy$.
- Step 2: Given $x + y = 10$, so $(x + y)^2 = 10^2 = 100$.
- Step 3: Given $xy = 21$, so $2xy = 2 \times 21 = 42$.
- Step 4: Compute $x^2 + y^2 = 100 - 42 = 58$.
- Step 5: Verify by checking options: Option (1) is 58, which matches.
- Step 6: Alternative check: If $x, y$ are roots of $t^2 - 10t + 21 = 0$, then $x^2 + y^2 = (x + y)^2 - 2xy = 58$.