Q. 344.3( 9 Votes )

# If x ≠ y ≠ z and

By properties of determinants, we can split the given determinant into 2 parts

Taking x, y, z common from R1, R2, R3 respectively

Operating R1R1-R3, R2R2- R3

Taking (x-z) and (y-z) common from R1, R2

Expanding with R3

y2+yz+z2-x2-xz-z2 = xyz(xy2+xyz+xz2+zy2+yz2+z3-x2y-xyz-yz2-x2z-xz2-z3)

(y-x)(y+x) +z(y-x) =xyz(xy2+zy2 -x2y -x2z)

(y-x)(x+y+z)=xyz(xy(y-x)+z(y2-x2))

(y-x)(x+y+z)= xyz(xy(y-x)+z(x+y)(y-x))

(y-x)(x+y+z) = xyz(xy(y-x)+(xz+yz)(y-x))

(y-x)(x+y+z)= xyz(y-x)(xy+xz+yz)

x+y+z = xyz(xy+xz+yz)

Hence Proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Using properties Mathematics - Board Papers

Using properties Mathematics - Board Papers

Using properties Mathematics - Board Papers

Prove the followiMathematics - Board Papers