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Grade 12Algebra

If x,y,z are in GP , then by using properties of determinants , show that
px+y x y
py+z y z = 0
o px+y py+z

Profile image of Sai Soumya
7 Years agoGrade 12
Answers icon

2 Answers

Profile image of Arun
7 Years ago
Dear student
 
put y = rx 
and
z = r^2 * x
 
then it will become very easy to solve by using determinant properties
Profile image of Aditya Gupta
7 Years ago
since x, y, z are in GP, y^2=xz
now multiply the first row by y and take 1/y common out of the determinant.
multiply the second row by x and take 1/x common out of the determinant.
now the 1st term of the 1st row is (px+y)*y= pxy+y^2= pxy+xz, which is equal to the 1st term of the 2nd row= (py+z)*x= pxy+xz
similarly the 2nd term of the 1st row is x*y which is equal to the 2nd term of the 2nd row=y*x
also third term of 1st row is y^2= xz which is equal to the 3rd term of the 2nd row= z*x
since row 1 is identical to row 2, hence the det is zero

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