CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Prove that:
∣ ∣a+b+2cabcb+c+2abcac+a+2b∣ ∣=2(a+b+c)3

Open in App
Solution

To prove:- ∣ ∣a+b+2cabcb+c+2abcac+a+2b∣ ∣=2(a+b+c)3
Proof:-
Taking L.H.S., we have
∣ ∣a+b+2cabcb+c+2abcac+a+2b∣ ∣

Applying C1C1+C2+C3, we get

=∣ ∣2a+2b+2cab2a+2b+2cb+c+2ab2a+2b+2cac+a+2b∣ ∣

=2(a+b+c)∣ ∣1ab1b+c+2ab1ac+a+2b∣ ∣

=2(a+b+c)[(b+c+2a)(c+a+2b)aba(c+a+2b)ab+abb(b+c+2a)]

=2(a+b+c)[(a+b+c)2+ab+a(c+a+2b)+b(b+c+2a)a(c+a+2b)abb(b+c+2a)]

=2(a+b+c)(a+b+c)2

=2(a+b+c)3

= R.H.S.

Hence proved.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon