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Interesting question

by netigen » Wed Apr 23, 2008 12:25 am
a+b = 5
a^2+b^2 = 9
What is the value of X = ab/(sqrt13-sqrt5)

1. 9/5(sqrt13-sqrt5)
2. 5/9(sqrt13-sqrt5)
3. 16/(sqrt13-sqrt5)
4. sqrt13+sqrt5
5. sqrt5-sqrt13
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by simplyjat » Wed Apr 23, 2008 1:19 am
a+b = 5
a^2+b^2 = 9
What is the value of X = ab/(sqrt13-sqrt5)

a^2+b^2 = (a+b)^2 - 2ab = 9
25 - 2ab = 9
2ab = 25 - 9 = 16
ab = 8

ab/(sqrt13-sqrt5)
= 8 / (sqrt13-sqrt5)
= 8 (sqrt13+sqrt5) / (13 - 5)
= (sqrt13+sqrt5)
...
simplyjat
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