BhandarkarA
Posts : 85
Join date : 2009-09-11
 | | Subject: Algebra Puzzle III Wed Dec 30, 2009 8:26 pm | |
| If the sum of two numbers (note that they may not be integers) is 10 and their product is 20. What is the sum of their squares? | |
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AK_Kadaveru
Posts : 28
Join date : 2009-10-20
| | Subject: Re: Algebra Puzzle III Thu Dec 31, 2009 1:34 pm | |
| - BhandarkarA wrote:
- If the sum of two numbers (note that they may not be integers) is 10 and their product is 20. What is the sum of their squares?
- Spoiler:
If one number is x, the other is 10-x so x(10-x)=20. what we are trying to find is x2+(10-x)2.
which is the same thing as x2+100+x2-20x or 100+2x2-20x. x(10-x)=20 so 10x-x2=20. if you multiply both sides by -2, you get -20x+2x2=-40. we are trying to find 100+2x2-20x. but we know -20x+2x2 =-40 so the answer is 60
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BhandarkarA
Posts : 85
Join date : 2009-09-11
| | Subject: Re: Algebra Puzzle III Thu Dec 31, 2009 2:25 pm | |
| My solution is similar, except it avoids the pesky squaring of (10-x): - Spoiler:
From the first statement, we have:
x+y=10
While from the second we have:
xy= 20
Let's square the first equation:
(x+y)^2=10^2
x^2+2xy+y^2=100
x^2+y^2+2(20)=100
x^2+y^2=60
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| | Subject: Re: Algebra Puzzle III | |
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