Surds and Indices Practice Test 2

Question : 12 of 17

Marks: +1, -0

Given that

abc = 1

, then find the value of

(1/{1+a+b^{-1}}

+1/{1+b+c^{-1}}

+1/{1+c+a^{-1}})

Solution:

1/{1+a+b^{-1}} +1/{1+b+c^{-1}} +1/{1+c+a^{-1}}

=1/{1+a+b^{-1}} +b^{-1}/{b^{-1}+1+b^{-1}c^{-1}} +a/{a+ac+1}

=1/{1+a+b^{-1}} +b^{-1}/{b^{-1}+1+a} +a/{a+b^{-1}+1}

(∵ abc=1⇒b^{-1}c^{-1}=a\;&\;b^{-1}=ac)

={1+a+b^{-1}}/{1+a+b^{-1}}=1

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