Question

If √6+√5/√6-√5=a+b√30,find the value of a and b in step by step process

Answer 1

Answer:

$\sf{The \ values \ of \ a \ and \ b \ are \ 11 \ and}$

$\sf{2 \ respectively. }$

Given:

$\sf{\dfrac{\sqrt6+\sqrt5}{\sqrt6-\sqrt5}=a+b\sqrt{30}}$

To find:

$\sf{The \ value \ of \ a \ and \ b.}$

Solution:

$\sf{a+b\sqrt{30}=\dfrac{\sqrt6+\sqrt5}{\sqrt6-\sqrt5}}$

$\sf{\therefore{a+b\sqrt{30}=\dfrac{(\sqrt6+\sqrt5)^{2}}{(\sqrt6-\sqrt5)(\sqrt6+\sqrt5)}}}$

$\sf{\therefore{a+b\sqrt{30}=\dfrac{6+5+2\sqrt{30}}{6-5}}}$

$\sf{\therefore{a+b\sqrt{30}=\dfrac{11+2\sqrt{30}}{1}}}$

$\sf{\therefore{a+b\sqrt{30}=11+2\sqrt{30}}}$

$\sf{On \ comparing \ we \ get,}$

$\sf{a=11 \ and \ b\sqrt{30}=2\sqrt{30}}$

$\sf{\therefore{a=11 \ and \ b=2}}$

$\sf\purple{\tt{\therefore{The \ values \ of \ a \ and \ b \ are \ 11 \ and}}}$

$\sf\purple{\tt{2 \ respectively. }}$