Home
Class 9
MATHS
If a^2 + b^2 + c^2 -ab-bc-ca = 0, then p...

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

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 a + b + c = 0 , then prove that (a+b)^2/(ab) + (b+c)^2/(bc) + (c+a)^2/(ca)=3

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

If a,b,c are positive unequal real numbers then prove that a^2+b^2+c^2gtab+bc+ca . Hence prove that a^3+b^3+c^3gt3abc

In the formula, a^3+b^3+c^3-3 abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca) if a + b + c = 0 , then show that a^3 + b^3 + c ^3 = 3 abc

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

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

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

∆ABC is right angled at C and CD _|_ AB . If BC = a , CA=b , AB = c and CD = p . Then prove that cp=ab

If x = b + c - 2a, y = c + a-2b , z = a + b-2c , then prove that x^3+y^3+z^3-3xyz=0

If the circles x ^2 + y ^2 + 2ax + c = 0 and x ^2 + y ^2 +2by + c = 0 touch each other, prove that 1/a ^2 + 1 b ^2 = 1/c

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

    |