Home
Class 11
MATHS
If x=a+b,y=aw+bw^2,z=aw^2+bw,show that x...

If x=a+b,`y=aw+bw^2`,`z=aw^2+bw`,show that `xyz=a^3+b^3`

Promotional Banner

Topper's Solved these Questions

  • MODEL QUESTION PAPERS-SET 12

    UNITED BOOK HOUSE|Exercise EXERCISE|49 Videos

  • MODEL QUESTION PAPERS-SET 14

    UNITED BOOK HOUSE|Exercise EXERCISE|49 Videos

Similar Questions

Explore conceptually related problems

IF x=a+bw+cw^2 , y=a+bw^2+cw then show that x^3+y^3=(2a-b-c)(2b-c-a)(2c-a-b)

If x=a+bw+cw^2 ,show that x^3-3ax^2+3(a^2-bc)x=a^3+b^3+c^3-3abc .when w be the an imaginarry cube root of unity.

If x=a+b,y=aomega+bomega^(2),z=aomega^(2)+bomega then show that xyz=a^(3)+b^(3) "where " omega is a complex cube root of 1 . Find square root of - 2i.

If a^(x)=b,b^(y)=c,c^(z)=a show that xyz =1 (a,b,c positive numbers)

(a) If x + y + z=0, show that x ^(3) + y ^(3) + z ^(3)= 3 xyz. (b) Show that (a-b)^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)

Answer any one question : If x : a = y : b = z : c, then show that (x^3)/(a^3) + (y^3)/(b^3) + (z^3)/(c^3) = (3xyz)/(abc) .

If x/a = y/b = z/c , then show that x^(3)/a^(3) + y^(3)/b^(3) + z^(3)/c^(3) = 3 ((x+y+z)/(a+b+c))^(3) .

If a^x=b, b^y=c,c^z=a then the value of xyz is

If x/a = y/b = z/c , then show that (x^(2)-yz)/(a^(2)-bc) = (y^(2)-zx)/(b^(2) - ca) = (z^(2)-xy)/(c^(2)-ab)

If x=a+b , y=aomega+bomega^2 , z=aomega^2+bomega then show that , x^3+y^3+z^3=3(a^3+b^3)

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 13-EXERCISE
  1. In a triangle ABC if a cos^2(C/2)+c cos^2(A/2)=((3b)/2)show that sides...

    Text Solution

    |

  2. Prove that by mathematical induction : 3^(2n+ 2) - 8n - 9 is divisible...

    Text Solution

    |

  3. If x=a+b,y=aw+bw^2,z=aw^2+bw,show that xyz=a^3+b^3

    Text Solution

    |

  4. if the ratio of the sum of n terms of two A Ps is (3n + 5) : (5n - 9)...

    Text Solution

    |

  5. The coefficient of three consecutive terms in the expansion of (1+x)^n...

    Text Solution

    |

  6. Show that the straight line (a + 2b) x + (a -3b)y + b -a = 0 always p...

    Text Solution

    |

  7. Find the equations of straight line which are perpendicular to the str...

    Text Solution

    |

  8. y = 2x is a chord of the circle x^2 + y^2 -10 x = 0. Find the equation...

    Text Solution

    |

  9. Find the ratio in which the plane 2x + 2y - 2z = 1 divides the line se...

    Text Solution

    |

  10. Evaluate :lim(xrarroo)[(1^(1//x)+2^(1//x)+3^(1//x))/3]

    Text Solution

    |

  11. Differentiate x^(-2/3) with respect to x, with behalf of definition.

    Text Solution

    |

  12. Prove that sqrt3is irrational, (use the method of contradiction)

    Text Solution

    |

  13. If x and y are odd integers, then xy is also an odd integer r examine ...

    Text Solution

    |

  14. The probability of occurrence of at least one event of two events X an...

    Text Solution

    |

  15. If the co-efficient of variation of two frequeny distribution are 58% ...

    Text Solution

    |

  16. Prove that (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

    Text Solution

    |

  17. In /\ABC,Prove that a cos A + b cos B + c cos C = 2a sin B sin C

    Text Solution

    |

  18. If a1,a2,a3,...,aaare in A.P then show that 1/(a1a2)+1/(a2a3)+1/(a3a4)...

    Text Solution

    |

  19. Solve x^2 -(7 -i)x + (18 -i) = 0 and hence prove that the roots are no...

    Text Solution

    |

  20. The Indian cricket eleven is to be selected out of 15 players. 6 of th...

    Text Solution

    |