Question

find the value of a and b if 5+√3/5-√3=a+b√15 ​

Answer 1

$\bold\color{red}{Answer:}$

$\rm{The~ value~ of ~(a+b) ~a ~is~ 20.}$

$\small\textbf{Step-by-step explanation:}$

$\color{red}\longrightarrow{}$$\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}=a+b\sqrt{15}$

$\color{red}\longrightarrow{}$$\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}=a+b\sqrt{15}$

$\color{red}\longrightarrow{}$$\frac{(\sqrt{5}+\sqrt{3})^2}{(\sqrt{5})^2-(\sqrt{3})^2}=a+b\sqrt{15}$

$\color{red}\longrightarrow{}$$\frac{5+2\sqrt{15}+3}{5-3}=a+b\sqrt{15}$

$\color{red}\longrightarrow{}$$\frac{8+2\sqrt{15}}{2}=a+b\sqrt{15}$

$\color{red}\longrightarrow{}$$4+\sqrt{15}=a+b\sqrt{15}$

$\rm{On~ comparing~ both~ sides.}$

a=4

b=1

The value of (a+b)a is

$\sf{(a+b)a=(4+1)4=5\times 4=20}$

$~~~~~~~~~~~~~$

$~~~~~~~~~~~~~$$\textbf\color{purple}\underline{the value of (a+b) a is 20.}$

─━─━─━─━─━─━─━─━─━─━─━─━─

Thankyou :)