Question

Find the value of a and b if " title="5+√3/7+2√3=a-b√3" alt="5+√3/7+2√3=a-b√3" align="absmiddle" class="latex-formula">

Answer 1

Answer:

The values of $a$ and $b$ are $5$ and $-\frac{15}{7}$, respectively.

Step-by-step explanation:

There are mistakes in the statement, correct form is presented below:

$5+\frac{\sqrt{3}}{7} + 2\sqrt{3} = a - b\cdot \sqrt{3}$.

By direct comparison we have the following system of equations:

$a = 5$ (1)

$\frac{\sqrt{3}}{7}+2\sqrt{3} = -b\cdot \sqrt{3}$ (2)

In (2) we solve for $b$:

$\left(\frac{1}{7}+2 \right)\cdot \sqrt{3} = -b\cdot \sqrt{3}$

$b = -\frac{15}{7}$

The values of $a$ and $b$ are $5$ and $-\frac{15}{7}$, respectively.