Enter the difference and product of two numbers to find them instantly!
Given:
Steps:
Solution:
1. Quadratic equation:
\( y^2 + 20y - 125 = 0 \)
2. Discriminant:
\( \sqrt{20^2 + 4 \cdot 125} = \sqrt{900} = 30 \)
3. Roots:
\( y_1 = \frac{-20 + 30}{2} = 5 \)
\( y_2 = \frac{-20 - 30}{2} = -25 \)
4. Calculate \( x \):
\( x = 20 + 5 = 25 \)
\( x = 20 - 25 = -5 \)
Result: The pairs of numbers are ( 25, 5) or (-5, -25).
Solution:
1. Quadratic equation:
\( y^2 + 11y - 1452 = 0 \)
2. Discriminant:
\( \sqrt{11^2 + 4 \cdot 1452} = \sqrt{5929} = 77 \)
3. Roots:
\( y_1 = \frac{-11 + 77}{2} = 33 \)
\( y_2 = \frac{-11 - 77}{2} = -44 \)
4. Calculate \( x \):
\( x_1 = 11 + 33 = 44 \)
\( x_2 = 11 - 44 = -33 \)
Result: The pairs of numbers are (44, 33) or (-33, -44).
Solution:
1. Quadratic equation:
\( y^2 + 7y - 450 = 0 \)
2. Discriminant:
\( \sqrt{7^2 + 4 \cdot 450} = \sqrt{1849} = 43 \)
3. Roots:
\( y_1 = \frac{-7 + 43}{2} = 18 \)
\( y_2 = \frac{-7 - 43}{2} = -25 \)
4. Calculate \( x \):
\( x_1 = 7 + 18 = 25 \)
\( x_2 = 7 - 25 = -18 \)
Result: The pairs of numbers are (25, 18) or (-18, -25).