Home
Class 12
MATHS
By using properties of determinants , s...

By using properties of determinants , show that : ` {:|( 1,x,x^(2) ),( x^(2) ,1,x) ,( x,x^(2), 1) |:} =( 1-x^(3)) ^(2) `

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    NCERT BANGLISH|Exercise EXERCISE 4.3|7 Videos

  • DETERMINANTS

    NCERT BANGLISH|Exercise EXERCISE 4.4|5 Videos

  • DETERMINANTS

    NCERT BANGLISH|Exercise EXERCISE 4.1|8 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 5|23 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISE|18 Videos

Similar Questions

Explore conceptually related problems

By using properties of determinats. Prove that- |(1,1+x,1+x+y),(2,3+2x, 1+3x+2y),(3,6+3x, 1+6x+3y):|= 1

Using properties of determinants porve that, |{:(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3):}|=(1+pxyz)(x-y)(y-z)(z-x)

|{:(3x^2,3x,1),(x^2+2x,2x+1,1),(2x+1,x+2,1):}|=(x-1)^3

Using the properties of proportion, solve for x, given (x^4+1)/(2x^2)=17/8 .

Show that lim_(x to 0)((1+x)^(9)-1)/((1+x)^(6)-1)=(3)/(2)

Without expanding a determinant at any stage, show that abs((x^2+x ,x+1 , x-2),(2x^2+3x-1 ,3x , 3x-3) , (x^2+2x+3, 2x-1 ,2x-1))=xA+B ,where A and B are determinant of order 3 not involving xdot

If y= (tan^(-1)x)^(2) , show that (x^(2)+1)^(2) y_(2)+2x(x^(2)+1)y_(1)=2 .

show that 2 tan ^(-1) ((1+x)/(1-x)) - cos ^(-1)( (1-x^(2))/(1+x^(2)))=(pi)/(2)

If g(x) = 1/x^2 , show that , g(x) - g(x + 1) = (2x + 1)/(x^2 (x + 1)^2) .

Without expanding show that the determinant |(1,a,a^2),(-1,2,4),(1,x,x^2)| has a factor (X-a)