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The roots of the equation 1/a+b+x = 1/a + 1/b + 1/x are a.

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sunniboy007
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The roots of the equation 1/a+b+x = 1/a + 1/b + 1/x are a. [#permalink] New post   29 Jan 2004, 15:21
The roots of the equation 1/a+b+x = 1/a + 1/b + 1/x are

a. a, b
b. a+b, a-b
c. -a, -b
d. 1/a+b, 1/a-b
e. Beats me!



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Re: The roots of the equation 1/a+b+x = 1/a + 1/b + 1/x are a. [#permalink] New post   29 Jan 2004, 16:05
Oh God , is there a way to keep myself from getting distracted. :-D

Anyway is it C) -a, -b
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Re: The roots of the equation 1/a+b+x = 1/a + 1/b + 1/x are a. [#permalink] New post   29 Jan 2004, 16:27
:cool

How did you work this one old chap?
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Re: The roots of the equation 1/a+b+x = 1/a + 1/b + 1/x are a. [#permalink] New post   29 Jan 2004, 16:37
Hi sunniboy, can I meet ur friends :lol: :lol: . Took me around 2 mins but I guess its the only way. Cross multiply, then u can cancel abx and then derive at the equation in the form of ax^2+bx+c=0, we get the equation (a+b)x^2 + (a+b)^2 x + ab(a+b), I think now u will be able to find out the roots. :-D
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Re: The roots of the equation 1/a+b+x = 1/a + 1/b + 1/x are a. [#permalink] New post   30 Jan 2004, 09:27
It might actually be simpler in this case to check one of each pair of roots - if one of them doesn't work - the answer choice is definitely wrong.

A) 1/a+b+a is not equal to 1/a + 1/b + 1/a - this is the concept that says that one cannot distribute a fraction under a common numerator...

B) for the same reason - 1/a+b+a+b is not 1/a + 1/b + 1/a+b for any a and b.

C) BUT - 1/a+b-a is just 1/b. 1/a + 1/b - 1/a is exactly the same. Ditto with -b. and you have your solution.

Lofty algebra is not always the right way to go - if it gets messy - look for an alternative....



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Re: The roots of the equation 1/a+b+x = 1/a + 1/b + 1/x are a. [#permalink]
30 Jan 2004, 09:27
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