AP and GP

Algebra Level 2

Let a , b , c a,b,c be numbers that follows an arithmetic progression in that order, and
let x , y , z x,y,z be numbers that follows a geometric progression in that order.

Find the value of x b − c ⋅ y c − a ⋅ z a − b x^{b-c} \cdot y^{c-a} \cdot z^{a-b} .


The answer is 1.

Deepanshu Dhruw by Deepanshu Dhruw , 21, India

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2 solutions

Deepanshu Dhruw
Jan 13, 2017

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Beautilful

Jerry McKenzie - 3 years, 4 months ago

if a = b − d a=b-d and c = b + d c=b+d , given relation becomes

y 2 d x d z d \frac{y^{2d}}{x^d z^d}

Which can be written as ( y 2 x z ) d (\frac{y^2}{xz})^d

This is evaluated using the fact that x,y,z are in G.P so y 2 = x z y^2=xz Thus the answer is 1

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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