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`        If x,y,z are in GP , then by using properties of determinants , show thatpx+y    x       ypy+z    y       z = 0o          px+y py+z`
one year ago

```							Dear student put y = rx andz = r^2 * x then it will become very easy to solve by using determinant properties
```
one year ago
```							since x, y, z are in GP, y^2=xznow 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+xzsimilarly the 2nd term of the 1st row is x*y which is equal to the 2nd term of the 2nd row=y*xalso third term of 1st row is y^2= xz which is equal to the 3rd term of the 2nd row= z*xsince row 1 is identical to row 2, hence the det is zero
```
one year ago
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