TS ICET 24 May 2018 Shift 1 Paper

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Question : 77 of 200

Marks: +1, -0

If a. b. c and d are non-zero real numbers such that

\a^x

=

\b^y=\c^z=\d^w

and ab=cd,then

1/\x - 1/\z =

$1/\y+1/\w$
$1/\y-1/\w$
$1/\w-1/\y$
1

Solution:

Let

a^{x}=b^{y}=c^{z}=d^{w}=p

⇒ a=p^{1 \/ x ; b}=p^{1 \/ y} ; c=p^{1 \/ z ; d}=p^{1 \/ w}

Given ab = cd

⇒ p^{1 \/ x} × p^{1 \/ y}=p^{1 \/ z} × p^{1 \/ w}

⇒ p^{(1 \/ x)+(1 \/ y)}=p^{(1 \/ z)+(1 \/ w)}

Equating the indices on equal bases, we get

\;{1}/{x}+{1}/{y}={1}/{z}+\;{1}/{w}⇒{1}/{x}-{1}/{z}={1}/{w}-{1}/{y}

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