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If \( a, b, c \) are three consecutive terms of an \( A P \) and \( x, y, z \) are three consecutive terms of a G.P.,
then thevalue of \( X^{b-c}, Y^{c-a}, Z^{a-b} \)
is
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then thevalue of \( X^{b-c}, Y^{c-a}, Z^{a-b} \)
is
Solution:
1662 Upvotes
Verified Answer
The correct answer is:
\( 1 \)
Given that, $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P. and $\mathrm{x}, \mathrm{y}, \mathrm{z}$ are in G.P.
Let $\mathrm{d}$ be the common difference between A.P. consecutive terms. So,
$b-a=c-b=d, c-a=2 d$
Now, $\chi^{b-c} \cdot y^{c-a} \cdot z^{a-b}$
$=x^{-d} \cdot y^{2 d} \cdot z^{-d}=(x z)^{-d} \cdot\left(y^{2}\right)^{-d}$
Since, $x z=y^{2}$ then $(x z)^{-d}(x z)^{d}=1$
Let $\mathrm{d}$ be the common difference between A.P. consecutive terms. So,
$b-a=c-b=d, c-a=2 d$
Now, $\chi^{b-c} \cdot y^{c-a} \cdot z^{a-b}$
$=x^{-d} \cdot y^{2 d} \cdot z^{-d}=(x z)^{-d} \cdot\left(y^{2}\right)^{-d}$
Since, $x z=y^{2}$ then $(x z)^{-d}(x z)^{d}=1$
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