Home
Class 12
MATHS
If x,y and z are different and Delta=|...

If x,y and z are different and
`Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3):}|=0` then show that `1+xyz=0`

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT PRAKASHAN|Exercise CHAPTER TEST (1 MARK QUESTIONS)|6 Videos

  • DETERMINANTS

    ARIHANT PRAKASHAN|Exercise CHAPTER TEST (4 MARK QUESTIONS)|7 Videos

  • DETERMINANTS

    ARIHANT PRAKASHAN|Exercise TOPIC -2 (PRACTICE QUESTIONS) (6 MARK QUESTIONS) |6 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT PRAKASHAN|Exercise Chapter test (6 mark question)|8 Videos

  • DIFFERENTIAL EQUATIONS

    ARIHANT PRAKASHAN|Exercise Chapter test (6 MARKS Questions)|8 Videos

Similar Questions

Explore conceptually related problems

Write the value of Delta=|{:(x+y,y+z,z+x),(z,x,y),(-3,-3,-3):}|

If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz=1 when x,y,z are non zero and unequal.

Show that |{:(1,x, x ^(3)),(1,y,y ^(3)),(1,z,z^(3)):}| = (x-y) (y-z) (z-x) (x + y + z)

Show that Delta =Delta_1 where Delta=|{:(Ax,x^2,1),(By,y^2,1),(Cz,z^2,1):}|,Delta_1=|{:(A,B,C),(x,y,z),(zy,zx,xy):}|

IF Delta=|{:(1,x,x^2),(1,y,y^2),(1,z,z^2):}| and Delta_1=|{:(1,1,1),(yz,zx,xy),(x,y,z):}| then prove that Delta +Delta_1=0

using the properties of determinants prove that |{:(1,x+y,x^2+y^2),(1,y+z,y^2+z^2),(1,z+x,z^2+x^2):}|=(x-y)(y-z)(z-x)

If [{:(x+y,x-z),(2x-y,0):}]=[{:(2,2),(1,0):}] ,find the value of x,y,z.

Using coafactors of the elements of third row, evaluate Delta=|{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|

If [{:(x-y,2x+z),(2x-y,3z+w):}]=[{:(-1,5),(0,13):}] then find x,y,z and w .

If "tan"^(-1) x +"tan" ^(-1) y +"tan"^(-1)z -pi show that x+y+z=xyz.