\( x^2 + y^2 = 10^2 - 2 \times 21 = 100 - 42 = 58 \)
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- If \( x \) and \( y \) are positive numbers such that \( x + y = 10 \) and \( xy = 21 \), what is the value of \( x^2 + y^2 \)?
- Use the identity: \( x^2 + y^2 = (x + y)^2 - 2xy \)
- Substitute \( x + y = 10 \) and \( xy = 21 \):
- A triangle has sides of length 7 cm, 24 cm, and 25 cm. Is it a right triangle? If so, what is its area?
- Check if it satisfies the Pythagorean theorem:
- \( 7^2 + 24^2 = 49 + 576 = 625 = 25^2 \)
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