find the value of a and b if 5+√3/5-√3=a+b√15
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5-√3=a+b√15
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[tex]\bold\color{red}{Answer:}[/tex]
[tex]\rm{The~ value~ of ~(a+b) ~a ~is~ 20.}[/tex]
[tex]\small\textbf{Step-by-step explanation:}[/tex]
[tex]\color{red}\longrightarrow{}[/tex][tex]\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}=a+b\sqrt{15}[/tex]
[tex]\color{red}\longrightarrow{}[/tex][tex]\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}=a+b\sqrt{15}[/tex]
[tex]\color{red}\longrightarrow{}[/tex][tex]\frac{(\sqrt{5}+\sqrt{3})^2}{(\sqrt{5})^2-(\sqrt{3})^2}=a+b\sqrt{15} [/tex]
[tex]\color{red}\longrightarrow{}[/tex][tex]\frac{5+2\sqrt{15}+3}{5-3}=a+b\sqrt{15} [/tex]
[tex]\color{red}\longrightarrow{}[/tex][tex]\frac{8+2\sqrt{15}}{2}=a+b\sqrt{15} [/tex]
[tex]\color{red}\longrightarrow{}[/tex][tex]4+\sqrt{15}=a+b\sqrt{15}[/tex]
[tex]\rm{On~ comparing~ both~ sides.}[/tex]
a=4
b=1
The value of (a+b)a is
[tex]\sf{(a+b)a=(4+1)4=5\times 4=20}[/tex]
[tex]~~~~~~~~~~~~~[/tex]
[tex]~~~~~~~~~~~~~[/tex][tex]\textbf\color{purple}\underline{the value of (a+b) a is 20.}[/tex]
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Thankyou :)