Question

if V5+√3/V5-V3= a-v15b, find the value of a and b?​

Answer 1

Answer:

a = ($\sqrt{5} -\sqrt{3}$)

b = -1/5

Step-by-step explanation:

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

= $\frac{\sqrt{5}.\sqrt{5}+\sqrt{3}-\sqrt{3} .\sqrt{5} }{\sqrt{5} } = a - \sqrt{15} b$

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

= $\frac{5+\sqrt{3}-\sqrt{15} }{\sqrt{5} }. (\frac{\sqrt{5} }{\sqrt{5} } ) = (a - b\sqrt{15} )$

= $\frac{(5+\sqrt{3}-\sqrt{15}). (\sqrt{5} ) }{\sqrt{5} . \sqrt{5} }= a - b\sqrt{15}$

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

= $\frac{5(\sqrt{5}-\sqrt{3})+\sqrt{15} }{5} = a - b\sqrt{15}$

=  $(\sqrt{5} - \sqrt{3} ) +\frac{\sqrt{15} }{5} = a - b\sqrt{15}$

=> a = $\sqrt{5} -\sqrt{3}$

=> b = $\frac{-1}{5}$