If a= \sqrt{5}+1}/\sqrt{5}-1} and b= \sqrt{5}-1}/\sqrt{5}+1}, then the value of a^2+ab+b^2 is

AP ICET 2016 Paper

Question : 92 of 200

Marks: +1, -0

a=\;\;{√{5}+1}/{√{5}-1}

and

b=\;\;{√{5}-1}/{√{5}+1}

, then the value of

a^2+ab+b^2

Solution:

,Given :

a=\;\;{√{5}+1}/{√{5}-1}

and

b=\;\;{√{5}-1}/{√{5}+1}

We have,

a^2+ab+b^2=(a+b)^2–ab

........(i)

=[{√{5}+1}/{√{5}-1}+{√{5}-1}/{√{5+1}}]^{2}-{√{5}+1}/{√{5}-1}×{√{5}-1}/{√{5+1}}

=[{(√{5}+1)^{2}+(√{5}-1)^{2}}/{(√{5}-1)(√{5}+1)}]^{-1}

=[{2\{(√{5})^{2}+1^{2}\}}/{5-1}]^{2}-1

=({2×6}/{4})^{2}-1=9-1=8

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