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

lf ∣∣ ∣ ∣∣xnxn+2xn+3ynyn+2yn+3znzn+2zn+3∣∣ ∣ ∣∣ =(x−y)(y−z)(z−x)(1x+1y+1z), then the value of n is

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

The correct option is B 1
∣ ∣ ∣xnxn+2xn+3ynyn+2yn+3znzn+2zn+3∣ ∣ ∣=xnynzn∣ ∣ ∣1x2x31y2y31z2z3∣ ∣ ∣
By row trasformation,
r1r1r2 and r3r3r2
=(xyz)n∣ ∣ ∣0(x2y2)(x3y3)1y2y30(z2y2)(z3y3)∣ ∣ ∣=(xyz)n(xy)(zy)∣ ∣ ∣0(x+y)(x2+xy+y2)1y2y30(z+y)(z2+zy+y2)∣ ∣ ∣
=(xyz)n(xy)(zy)[1(x+y)(z2+zy+y2)(z+y)(x2+xy+y2)]
=(xyz)n(xy)(yz)[xz2+xyz+xy2+yz2+zy2+y3[zx2+xyz+zy2+yx2+xy2+y3]]
=(xyz)n(xy)(yz)(xz2zx2yx2+yz2)
=(xyz)n(xy)(yz)(zx(zx)+y(zx)(z+x))
=(xyz)n(xy)(yz)(zx)(xz+yz+xy)
=(xyz)n+1(xy)(yz)(zx)(1x+1y+1z)
So, (x+y+z)n+1=1
n+1=0
n=1

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