BhandarkarA
Posts : 85
Join date : 2009-09-11
 | | Subject: Algebra puzzle Wed Dec 30, 2009 8:21 pm | |
| If ac=5, bc=2, and ab=10, find the value of a^2+b^2+c^2. | |
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AK_Kadaveru
Posts : 28
Join date : 2009-10-20
| | Subject: Re: Algebra puzzle Thu Dec 31, 2009 1:07 pm | |
| - BhandarkarA wrote:
- If ac=5, bc=2, and ab=10, find the value of a^2+b^2+c^2.
The answer is: - Spoiler:
30
Explanation: - Spoiler:
b is double of c because ac=5 and ab=10. that means b=2c and bc=2 (given) so 2c2=2 and c=1.
then b=2 so a=5. then a2+b2+c2=52+22+12=25+4+1=30
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BhandarkarA
Posts : 85
Join date : 2009-09-11
| | Subject: Re: Algebra puzzle Thu Dec 31, 2009 2:21 pm | |
| @AK_Kadaveru: Correct. c could be either + or - 1 by your logic, but in the end you get the same answer. An alternate solution: - Spoiler:
(ab)(ac)/bc=a^2, so a^2= 25
(ab)(bc)/ac=b^2, so b^2= 4
(bc)(ac)/ab=c^2, so c^2= 1
There sum being 25+4+1 we get 30.
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