Math, asked by vaitlasiddartha7, 9 months ago

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

Answers

Answered by Anonymous
6

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. }}

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