Answer:
[tex]a=\frac{7}{2} \ \ ,\ \ \ b=\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]\frac{2}{7+3\sqrt{5} } =\frac{2\times \left( 7-3\sqrt{5} \right) }{\left( 7+3\sqrt{5} \right) \left( 7-3\sqrt{5} \right) }[/tex]
[tex]=\frac{2\times \left( 7-3\sqrt{5} \right) }{7^{2}-\left( 3\sqrt{5} \right)^2 }[/tex]
[tex]=\frac{2\times \left( 7-3\sqrt{5} \right) }{49-45 }[/tex]
[tex]=\frac{2\times \left( 7-3\sqrt{5} \right) }{4 }[/tex]
[tex]=\frac{7-3\sqrt{5} }{2 }[/tex]
[tex]=\frac{7}{2} -\frac{3}{2} \sqrt{5}[/tex]
Then
a = 7/2
b = 3/2
