Question

A sum of two numbers is 10 and their square is 80 use this quadratic equation information to form quadratical equations

Answer 1

let the two numbers be x and y
x  + y = 10
x² + y² = 80
Express x in terms of y
x = 10 - y
(10 - y)² + y² = 80
100 - 20y + y² + y² = 80
100 - 20y + 2y² - 80 = 0
2y² - 20y + 20 = 0
divide through by 2
y² - 10y + 10 = 0

we can also formulate another quadratic equation in terms of x by expressing y in terms of x
y = 10 - x
substituting in the second equation
x² + (10 - x)² = 80
x² + 100 - 20x + x² = 80
x² + 100 - 20x + x² - 80 = 0
2x² - 20x + 20 = 0
divide through by 2
x² - 10x + 10 = 0

Answer 2

y2-10y+10