SOLUTION: If the sum of the squares of two numbers is 120, while their product is 24. What is their difference?

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Question 1121419: If the sum of the squares of two numbers is 120, while their product is 24. What is their difference?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x and y are the numbers
x^2+y^2=120
xy=24
x=24/y; substitute
576/y^2+y^2=120
multiply through by y^2
y^4-120y^2+576=0
y^2=(1/2)(120+/-sqrt(120^2-2304)); sqrt term=109.99
y^2=(1/2)(229.99) or 115 and y^2=(1/2)(10.01) or 5
y=sqrt (115) or 10.72 x=sqrt(5) or 2.24
to three decimal places,
x=2.237
y=10.723
product 23.987
sum of squares 119.987
Their difference is 8.486

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
x^2 + y^2 = 120,     (1)
xy        =  24.     (2)


=====>  x^2 - 2xy + y^2 = 120 - 2*24 = 120 - 48 = 72  ====>  %28x-y%29%5E2 = 72  


====>  x - y = +/- sqrt%2872%29.

Solved.