SOLUTION: Find two numbers such that their sum is 10 and their product is 22.

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Question 101116This question is from textbook Algebra for College Students
: Find two numbers such that their sum is 10 and their product is 22. This question is from textbook Algebra for College Students

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
A)x+y=10
B)xy=22
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y=22/x from B)
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x+(22/x)=10 substitute 22/x for y in A)
x^2+22=10x multiply x times each side.
x^2-10+22=0
Quadratic formula: x=5+sqrt(3) or x=5-sqrt(3)
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When x=5+sqrt(3) y=10-(5+sqrt(3))=10-5-sqrt(3)=5-sqrt(3)
When x=5-sqrt(3) y=10-(5-sqrt(3))=10-5+sqrt(3)=5+sqrt(3)
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Check:
5+sqrt(3)+5-sqrt(3)=10
(5+sqrt(3))*(5-sqrt(3))=25-3=22
Ed