wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Given, x=cy+bz,y=az+cx,z=bx+ay, where x, y, z are not all zero, and a, b, c are real numbers. The value of a2+b2+c2+2abc is

A
\N
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 1
Given systems of equations can be rewritten as
x+cy+by=0,cxy+az=0 and bx+ayz=0
Above system of equations are homogeneous equation. Since, x, y and z are not all zero, so it has non - trivial solution.
Therefore, the coefficient of determinant must be zero.
∣ ∣1cbc1aba1∣ ∣=0
1(1a2)c(cab)+b(ca+b)=0
a2+b2+c2+2abc1=0
a2+b2+c2+2abc=1

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