ammuseeru wrote:
Could you help me with following question.
If \(a^2\) – \(ab\) = \(2b^2\), which of the following could be b/a ?
I. \(1/2\)
II. \(2\)
III. \(-1\)
(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III
HI..
If you are seeing an equation in terms of variables and value asked in terms of fraction, try dividing the equation by the variable in denominator..here divide equation \(a^2\) – \(ab\) = \(2b^2\) by \(a^2..\)..
so \(\frac{a^2-ab}{a^2}=\frac{2b^2}{a^2}.......... 1-\frac{b}{a}=2*\frac{b}{a}^2\)..
here you can do two things ..
(A) substitute the given values ..\(1-\frac{b}{a}=2*\frac{b}{a}^2\)..
1) 1/2..
\(1-\frac{1}{2}=2*\frac{1}{2}^2........1-1/2=1/2\)...YES
2) 2..
\(1-2=2*2^2\).....No
3) -1
\(1-(-1)=2*(-1)^2....1+1=2\).....YES
so I and III
D
(B) solve ..\(1-\frac{b}{a}=2*\frac{b}{a}^2\)..
let b/a = x..
so \(1-x=2x^2.....2x^2+x-1=0....(2x-1)(x+1)=0\)..
so x=1/2 or x=-1
D
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