If {2+\sqrt{3}/{2-\sqrt{3}+ {2-\sqrt{3}/{2+\sqrt{3}+ \sqrt{3}-1}/\sqrt{3}+1}=a+b\sqrt{3},then a+4b=

AP ICET 2016 Paper

Question : 86 of 200

Marks: +1, -0

\;\;{2+√{3}}/{2-√{3}}+\;\;{2-√{3}}/{2+√{3}}+\;\;{√{3}-1}/{√{3}+1}=a+b√{3}

,then

a+4b=

Solution:

Given :

{2+√{3}}/{2-√{3}}+{2-√{3}}/{2+√{3}}+{√{3}-1}/{√{3}+1}=a+b√{3}

L.H.S

={(2+√{3})^{2}+(2-√{3})^{2}}/{(2-√{3})(2+√{3})}+{(√{3-1})^{2}}/{(√{3})^{2}-1}

={2[2^{2}+(√{3})^{2}]}/{4-3}+{3+1-2√{3}}/{3-1}

=14+{4-2√{3}}/{2}=14+2-√{3}=16-√{3}

⇒16-√3=a+b√3,a=16,b=-1

∴a+4b=16+4(-1)=12

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