Home
Class 9
MATHS
If x^(1/3)+y^(1/3)+z^(1/3)=0, then prove...

If `x^(1/3)+y^(1/3)+z^(1/3)=0`, then prove that `(x+y+z)^3=27xyz`

Promotional Banner

Topper's Solved these Questions

  • HARDER PRODUCT AND FACTORISATION

    KALYANI PUBLICATION|Exercise EXERCISE|148 Videos

  • GEOMETRY

    KALYANI PUBLICATION|Exercise EXERCISE|10 Videos

  • INEQUALITIES AND INEQUATIONS

    KALYANI PUBLICATION|Exercise EXERCISE|126 Videos

Similar Questions

Explore conceptually related problems

If cos^(-1) x +cos^(-1)y +cos^(-1)z =pi , then prove that x^(2)+y^(2)+z^(2)+2xyz=1 .

If (3.7)^x=(.37)^y=1000 ,then prove that 1/x-1/y=1/3

If x = 10 , y = 64, and z = 2, then prove that (x+y+z)^3 = 438976

If a,b,c are in G.P and a^(1/x)=b^(1/y)=c^(1/z) then prove that x,y,z are in A.P.

If x = 658, y = 668, z = 674 , then prove that x^3+y^3+z^3-3xyz=392000

If x+y+z=6 , and xy+yz+zx=12 , then prove that x^3+y^3+z^3=3xyz

If tan^-1 x+tan^-1 y+tan^-1 z=pi , prove that x+y+z=xyz

If 3x + 2y = -1 , then prove that 27x^3+8y^3+1-18xy = 0

If log((x+y)/3)=1/2(logx+logy) ,then prove that x/y+y/x=7

If sin^-1 x+sin^-1 y +sin^-1 z=pi/2 , prove that x^2+y^2+z^2+2xyz=1 .

KALYANI PUBLICATION-HARDER PRODUCT AND FACTORISATION -EXERCISE
  1. If x-y=7and xy=9, then find the value of (x^2+y^2)

    Text Solution

    |

  2. Prove that 4x^2(y-z)+y^2(2x-z)+z^2(2x+y)-4xyz = (2x+y)(y-z)(2x-z)

    Text Solution

    |

  3. Prove that (x-a)^2/((a-b)(a-c))+(x-b)^2/((b-a)(b-c))+(x-c)^2/((c-a)(...

    Text Solution

    |

  4. Prove that 1/(a(a-b)(a-c))+1/(b(b-c)(b-a))+1/(c(c-a)(c-b))=1/(abc)

    Text Solution

    |

  5. Prove that a/(bc(a-b)(a-c))+b/(ca(b-c)(b-a))+c/(ab(c-a)(c-a))=1/(abc...

    Text Solution

    |

  6. Prove that 2(s-a)(s-b)(s-c)+a(s-b)(s-c)+b(s-c)(s-a)+c(s-a)(s-b)=abc ...

    Text Solution

    |

  7. Factorise a^3-b^3+1+3ab

    Text Solution

    |

  8. If a + b + c = 0, then prove that 1/(2a^2+bc)+1/(2b^2+ca)+1/(2c^2+a...

    Text Solution

    |

  9. If a^2 + b^2 + c^2 -ab-bc-ca = 0, then prove that a=b=c

    Text Solution

    |

  10. If a + b + c = 0, then prove that (a+b)^2/(ab) + (b+c)^2/(bc) + (c+...

    Text Solution

    |

  11. If a + b + c = 0, then prove that (2a^2)/(a^2-b^2-c^2)+(2b^2)/(b^2-...

    Text Solution

    |

  12. If a + b + c = 0, then prove that (a^2+b^2+c^2)/(a^3+b^3+c^3)+2/3(1...

    Text Solution

    |

  13. If a+b=c then prove that 1/(b^2+c^2-a^2)+1/(c^2+a^2-b^2)+1/(a^2+b^2...

    Text Solution

    |

  14. If a+b+c=0, then prove that a(c+a)(a+b)=b(a+b)(b+c)=c(a+c)(b+c)=abc

    Text Solution

    |

  15. If a+b+c=0, then prove that a(b+c)^2+b(c+a)^2+c(a+b)^2=3abc

    Text Solution

    |

  16. If A=ax+by+cz, B=bx+cy+az, C=cx+ay+bz and a+b+c=0, then prove that A...

    Text Solution

    |

  17. If x^(1/3)+y^(1/3)+z^(1/3)=0, then prove that (x+y+z)^3=27xyz

    Text Solution

    |

  18. If a+b+c=0, then prove that a^4+b^4+c^4=2(ab+bc+ca)^2

    Text Solution

    |

  19. If a+b+c=0, then prove that (a^2+b^2+c^2)^2=4 (a^2b^2+b^2c^2+c^2a^2)

    Text Solution

    |

  20. If a+b+c=0, then prove that a(b+c)^2+b(c+a)^2+c(a+b)^2=3abc

    Text Solution

    |