What progression?

Algebra Level 4

3 x 2 − 2 ( a − d ) x + ( a 2 + 2 ( b 2 + c 2 ) + d 2 ) = 2 ( a b + b c + c d ) 3x^2 - 2(a-d)x + (a^2 +2(b^2 +c^2) + d^2) = 2(ab + bc + cd)

Given the above equation, what type of progression does a , b , c a,b,c and d d follow?

Arithmetic progression None of these choices Harmonic progression Geometric progression

Pankaj Joshi by Pankaj Joshi , 23, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

3x^{2} - 2x(a-d) + (a^{2} + b^{2} - 2ab ) + (b^{2} + c^{2} - 2bc ) + (c^{2} + d^{2} - 2cd ) = 0
3x^{2} - 2x{(a-b) + (b - c) + (c - d)} + (a- b)^{2} + (b - c)^{2} + (c - d)^{2} = 0
x^{2} - 2x(a-b) + (a- b)^{2} + x^{2} - 2x(b-c) + (b-c)^{2} + x^{2} - 2x(c-d) + (c-d)^{2} = 0
(x - a + b)^{2} +(x - b + c)^{2} +(x - c + d)^{2} = 0..Square terms are >=0
Hence each bracket = 0. So x = a - b = b - c = c - d.....A.P.

1 Helpful 1 Interesting 0 Brilliant 0 Confused
Hemang Sarkar
Jul 8, 2014

(x-a+b)^2 + (x-b+c)^2 + (x-c+d)^2 = 0. therefore, b-a=c-b=d-c. hence AP.

2 Helpful 0 Interesting 0 Brilliant 1 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...