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Algebra Level 3

two non-real number, a a and b b , satisfy a b = a − b ab= a-b . possible value of a / b + b / a − a b a/b + b/a - ab .


The answer is 2.

Rakshit Joshi by Rakshit Joshi , 26, India

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1 solution

Zhaochen Xie
Oct 27, 2015

Since most non-real solution problem works too if u find real solution, so plugging in a=1 and b=1/2 would be a quick way to solve it

2 Helpful 0 Interesting 0 Brilliant 0 Confused

yes I too did the same manner but how to do it algebrically

Rakshit Joshi - 5 years, 7 months ago

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Given that a b = a − b ab=a-b we have a 2 b 2 = a 2 + b 2 − 2 a b a^2b^2=a^2+b^2-2ab

So the expression a b + b a − a b = a 2 + b 2 a b − a b = a 2 b 2 + 2 a b a b − a b = 2 \frac{a}{b}+\frac{b}{a}-ab = \frac{a^2+b^2}{ab}-ab = \frac{a^2b^2+2ab}{ab}-ab = 2

Sachin Sharma - 5 years, 7 months ago

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Nice solution sachin!!

Rakshit Joshi - 5 years, 7 months ago

me too bro

Saiful Haque - 5 years, 7 months ago

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