Question

Find the value of a' and 'b' if 2/ 7+3√5 =a-b√5​

Answer 1

Answer:

$a=\frac{7}{2} \ \ ,\ \ \ b=\frac{3}{2}$

Step-by-step explanation:

$\frac{2}{7+3\sqrt{5} } =\frac{2\times \left( 7-3\sqrt{5} \right) }{\left( 7+3\sqrt{5} \right) \left( 7-3\sqrt{5} \right) }$

         $=\frac{2\times \left( 7-3\sqrt{5} \right) }{7^{2}-\left( 3\sqrt{5} \right)^2 }$

         $=\frac{2\times \left( 7-3\sqrt{5} \right) }{49-45 }$

         $=\frac{2\times \left( 7-3\sqrt{5} \right) }{4 }$

         $=\frac{7-3\sqrt{5} }{2 }$

         $=\frac{7}{2} -\frac{3}{2} \sqrt{5}$

Then

a = 7/2

b = 3/2

Answer 2

Step-by-step explanation:

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