Question

Find the value of a and b in 5+2√3÷ 7+4√3 = a + b√3. for class 9.​

Answer 1

Answer:

$a = 23 \\ b = - 13$

Step-by-step explanation:

$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = \frac{(5 + \sqrt{3} )(7 - 4 \sqrt{3} )}{ {7}^{2} - {(4 \sqrt{3} )}^{2} } \\ \\ = \frac{35 - 20 \sqrt{3} + 7 \sqrt{3} - 4 \times 3}{49 - 48} \\ \\ = 35 - 12 - 13 \sqrt{3 } \\ \\ = 23 - 13 \sqrt{3} = a + b \sqrt{3} \\ \\ a = 23 \\ b = - 13$

Answer 2

Step-by-step explanation:

\begin{lgathered}a = 23 \\ b = - 13\end{lgathered}

Step-by-step explanation:

\begin{lgathered}\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = \frac{(5 + \sqrt{3} )(7 - 4 \sqrt{3} )}{ {7}^{2} - {(4 \sqrt{3} )}^{2} } \\ \\ = \frac{35 - 20 \sqrt{3} + 7 \sqrt{3} - 4 \times 3}{49 - 48} \\ \\ = 35 - 12 - 13 \sqrt{3 } \\ \\ = 23 - 13 \sqrt{3} = a + b \sqrt{3} \\ \\ a = 23 \\ b = - 13\end{lgathered}