If \(\frac{a}{b}\) + \(\frac{b}{a}\) = 2
Find a - b
Answer & explanation
Correct answer: option 1
Formula → x + \(\frac{1}{x}\) = 2, then x = 1 always
Put \(\frac{a}{b}\) = 1
\(\frac{b}{a}\) = 1
then a - b = 0
Method 2 → \(\frac{a}{b}\) + \(\frac{b}{a}\) = 2
\(\frac{a^2 + b^2}{ab}\) = 2
a2 + b2 = 2ab
a2 + b2 - 2ab = 0
(a - b)2
So, a = b → Put in question.
\(\frac{a}{a}\) + \(\frac{a}{a}\) = 2 (satisfied)