If the sum of two numbers is 13 and the sum of their square is 85. Find the…

Solution:

• Let the two numbers be x and 13 - x.

• Form the equation from the given sum of squares: x^2 + (13 - x)^2 = 85.

• Expand: x^2 + (13 - x)^2 = x^2 + 169 - 26x + x^2 = 85.

• Simplify: 2x^2 - 26x + 169 = 85 ⇒ 2x^2 - 26x + 84 = 0.

• Divide by 2: x^2 - 13x + 42 = 0.

• Factor: (x - 6)(x - 7) = 0, so x = 6 or x = 7.

• Thus the two numbers are 6 and 7 (in either order).