AP ICET 2017 Shift 1 Paper

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Question : 76 of 200

Marks: +1, -0

{X}=\;\;{a-b}/{a+b},{Y}=\;\;{b-c}/{b+c},{Z}=\;\;{c-a}/{c+a}⇒\;\;{1+x}/{1-x}⋅\;\;{1+y}/{1-y}⋅\;\;{1+z}/{1-z}=

0
$a+b+c$
$ab+bc+ca$
1

Solution:

1+x={(a-b)+(a+b)}/{a+b}=\;{2a}/{a+b}

1-x={(a-b)-(a-b)}/{a+b}={2b}/{a+b}

⇒{1+x}/{1-x}={2a}/{a+b}⋅{a+b}/{2b}={a}/{b}

Similarly

{1+y}/{1-y}={b}/{c}

and

{1+z}/{1-z}={c}/{a}

∴{1+x}/{1-x}⋅{1+y}/{1-y}⋅{1+z}/{1-z}=\;\;{a}/{b}⋅{b}/{c}⋅{c}/{a}=1

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