Geometric Progression

The correct answer is B:Negative
Given that;

a%2Cb%2Cc

are distinct positive numbers
By using

AM%E2%89%A5GM

x%2By%E2%89%A52%5Csqrt%7Bxy%7D

y%2Bz%E2%89%A52%5Csqrt%7Byz%7D

z%2Bx%E2%89%A52%5Csqrt%7Bzx%7D

So,

(x%2By)(y%2Bz)(z%2Bx)%E2%89%A52%5Csqrt%7Bxy%7D.2%5Csqrt%7Byz%7D.2%5Csqrt%7Bzx%7D

⇒

(x%2By)((y%2Bz)(z%2Bx)%E2%89%A58(xyz)

Now let

x%3Db%2Bc-a%2C%5Cspace%20y%3Dc%2Ba-b%2C%5Cspace%20z%3Da%2Bb-c

x%2By%3D2c%2C%5Cspace%20y%2Bz%3D2a%2C%5Cspace%20z%2Bx%3D2b

%5Ctherefore%20(2a)(2b)(2c)%E2%89%A58(b%2Bc-a)(c%2Ba-b)(a%2Bb-c)

⇒

(b%2Bc-a)(c%2Ba-b)(a%2Bb-c)-abc%E2%89%A40%5Cspace%20(negative)

Chapter Questions
1 MCQs