Question

, if a b c d are in continued proportion then prove that B minus C whole square + c minus a whole square + d minus b whole square is equals to a minus d whole square

Answer 1

Answer:

d-a the whole square

Step-by-step explanation:

Answer 2

Answer:

a,b,c and d are in continued proportion.

This means a/b=b/c=c/d.

Therefore b^2=ac, c^2=bd, bc=ad

BY USING THIS FORMULA:-

a^2+b^2+c^2 =(a+b+c)^2-2(ab+bc+ca)

LHS: (b-c)^2+(c-a)^2+(d-b)^2

Putting the values of a,b and c in the equation we get:

(a+b+c)^2-2(ab+bc+ca)

=(b-c+c-a+d-b)^2-2(bc-ba-c^2++ca+cd-bc-ad+ab+bd-b^2-cd+cb)

=(-a+d)^2-2(ca-ad+bd-b^2)

=a^2 +d^2-2ad-2ca-2bd +2b^2+2ad

=a^2+2b^2+d^2-2ca-2bd---------------------------------(equn1)

¶Putting the values of b^2,c^2,bc=ad in equation 1 we get,

=a^2+2ac+d^2-2ca-2ad

=a^2+d^2-2ad

=(a-d)^2 HENCE PROVED.

LHS=RHS=(a-d)^2.

From Samannay Roy.