Question

If x + y = 10 and xy = 21, what is x² + y²?

• A. 58
• B. 64
• C. 72
• D.

Hint:

Use the identity x^2 + y^2 = (x + y)^2 - 2xy for sum of squares problems.

Answer 1

The Correct Option is A

To find the value of \(x^2 + y^2\), we start with the given equations: \(x + y = 10\) and \(xy = 21\).

We can use the identity:

\[x^2 + y^2 = (x + y)^2 - 2xy\]

By substituting the given values into this identity:

\[(x + y)^2 = 10^2 = 100\]

\[2xy = 2 \times 21 = 42\]

Subtracting these, we get:

\[x^2 + y^2 = 100 - 42 = 58\]

Thus, the value of \(x^2 + y^2\) is \(\textbf{58}\).