Question:
If x + y = 10 and xy = 21, what is x2 + y2?
If x + y = 10 and xy = 21, what is x2 + y2?
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Use the identity x^2 + y^2 = (x + y)^2 - 2xy for sum of squares problems.
Updated On: Aug 11, 2025
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The Correct Option is A
Solution and Explanation
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 \(\textbf{58}\).
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