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

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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

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y2-10y+10
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