সমাধান কর: $\frac{x}{a}+\frac{a}{x}=\frac{x}{b}+\frac{b}{x}$

Question

সমাধান কর: $\dfrac{x}{a}+\dfrac{a}{x}=\dfrac{x}{b}+\dfrac{b}{x}$

Answer 1

$\dfrac{x}{a}+\dfrac{a}{x}=\dfrac{x}{b}+\dfrac{b}{x}$

বা, $\dfrac{x}{a}-\dfrac{x}{b}=\dfrac{b}{x}-\dfrac{a}{x}$

বা, $\dfrac{bx-ax}{ab}=\dfrac{b-a}{x}$

বা, $\dfrac{x\left(b-a\right)}{ab}=\dfrac{b-a}{x}$

বা, $\dfrac{x\left(b-a\right)}{ab}\times\dfrac{1}{\left(b-a\right)}=\dfrac{b-a}{x}\times\dfrac{1}{\left(b-a\right)}$

বা, $\dfrac{x}{ab}=\dfrac{1}{x}$

বা, $x^2=ab$

$\therefore x=\sqrt{ab}$

সুতরাং নির্ণেয় সমাধান $x=\sqrt{ab}$ [Answer]