If \(\frac{a}{b}\) + \(\frac{b}{a}\) = 2

Find a - b

0

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)