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Please refer to a Proof given in the Explanation Given that, a^x=b^y=c^z=d^u Suppose that, a^x=b^y=c^z=d^u=k a=k^(1/x), b=k^(1/y), c=k^(1/z), and, d=k^(1/u)(1) Now, a, b, c, and, d are in GP b/a=c/b=d/c. G V X è ¹ ) Q } ' JH V SF x * þ § Ð r g q % 3 y V r g w A $ p K < t ¤ r g w Ã Ô b } * þ § Ð r g q x h þ Í w ± ö S § Ð ` Ï ú w ² x l V ^ d r g p K ð} h % 3 y V r g q x 7 ú w ô M ñ S ¬ w ñ S ¯ ï Ä å µ Ä !. 62 = H > B R G B D g Z F b g g h _ h e h ` d b y m g b \ _ j k b l _ l “ K \ B \ Z g J b e k d b”, L h f 53, K \I 1 1, F _ o Z g b a Z p b y, _ e _ d l j b n.

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Example 22 If a, b, c are in GP and "a" ^(1/𝑥) = "b" ^(1/𝑦) = "c" ^(1/𝑧) , prove that x, y, z are in AP Given that "a" ^(1/𝑥) = "b" ^(1/𝑦) =. 񗿗 ɏ㋍ @1,600 ~ @1,000 ~ ` Y g @750 ~ h @1,600 ~. ̖{ ̐ ͂ o A n Ə ɖ ₩ Ȃӂ 甧 ւƓ n C r X J X G L X Ղ ґ X y V P A Z b g A K ʂ ̕ ɂƂ y Ȃ 炨 S ̂ɗǂ Ȃ ܂ Ă B ̊ Ђǂ ꍇ ͈ x Ȃ ܂ A J Ԃ 񂲎g p B n C r X J X G b Z X.

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