Question

A√3- b√3/ab=6 знайти 1/b-1/a

Answer 1

Ответ:

Смотри решение на фото

Answer 2

To find the value of $\frac{1}{b} - \frac{1}{a}$, we first need to solve the given equation $A\sqrt{3} - \frac{B\sqrt{3}}{AB} = 6$ for $\frac{1}{b} - \frac{1}{a}$.

Let's start by simplifying the given equation: $A\sqrt{3} - \frac{B\sqrt{3}}{AB} = 6$

To simplify the equation, we can take $\sqrt{3}$ as a common factor from the first two terms on the left-hand side: $\sqrt{3}(A - \frac{B}{AB}) = 6$

Now, let's simplify the term $\frac{B}{AB}$. Since $\frac{B}{AB} = \frac{1}{A}$, the equation becomes: $\sqrt{3}(A - \frac{1}{A}) = 6$

Now, we can divide both sides by $\sqrt{3}$ to isolate $A - \frac{1}{A}$: $A - \frac{1}{A} = \frac{6}{\sqrt{3}}$

To further simplify, we can rationalize the denominator on the right-hand side: $A - \frac{1}{A} = \frac{6}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{6\sqrt{3}}{3} = 2\sqrt{3}$

Now that we know the value of $A - \frac{1}{A}$, we can find $\frac{1}{b} - \frac{1}{a}$: $\frac{1}{b} - \frac{1}{a} = \frac{A - \frac{1}{A}}{B}$

Substitute the value of $A - \frac{1}{A} = 2\sqrt{3}$ and solve for $\frac{1}{b} - \frac{1}{a}$: $\frac{1}{b} - \frac{1}{a} = \frac{2\sqrt{3}}{B}$