SOLUTION: Sherlock Hemlock thought of two numbers. Their sum was 20 and the sum of their squares was 300. What was their product?
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Question 230473: Sherlock Hemlock thought of two numbers. Their sum was 20 and the sum of their squares was 300. What was their product?
Found 2 solutions by checkley77, solver91311:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
Their sum was 20 and the sum of their squares was 300.
What was their product?
x^2+y^2=300
x+y=20 square both sides of this equation.
x^2+2xy^y^2=400 now subtract the first equation
-(x^2+y^2=300)
--------------------
2xy=100
xy=100/2
xy=50 ans.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Substitute:
^2\ +\ y^2\ =\ 300)
 \pm sqrt{(-20)^2 - 4(1)(50)}}{2(1)} )
Verification of the last two steps left as an exercise for the student.
Product is then the difference of 2 squares:
\left(10\ \mp\ 5\sqrt{2}\right)\ =\ 100\ -\ 50\ =\ 50)
John
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