Home
Class 11
MATHS
Let a, b, c, d be real numbers in G.P. ...

Let `a, b, c, d` be real numbers in `G.P.` If `u, v, w` satisfy the system of equations `u + 2v +3w = 6,4u + 5v + 6w =12 and 6u + 9v = 4` then show that the roots of the equation`(1/u+1/v+1/w)x^2+[(b-c)^2+(c-a)^2+(d-b)^2]x+(u+v+w)=0` and `20x^2+10(a-d)^2 x-9=0` are reciprocals of each other.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

If the cube roots of unity are 1, omega, omega ^(2) then the roots of the equation (x-2) ^(3)+ 27=0 are-

If u and v are real numbers and (u+3)^(2)+(v+5)^(2)=0 , then find the values of u and v.

If (u^2+v^2) prop (x^2 +y^2 ) and uv prop xy then show that (u+v) prop (x+y) when u/v+v/u=x/y +y/x .

If 3u + 4v =10 nd S_u = 1.2 . then Var (v) = 0.81

If the roots of the equation x^(3) -10 x + 11 = 0 are u, v, and w, then the value of 3 cosec^(2) (tan^(-1) u + tan^(-1) v + tan^(-1) w) is ____

Show that the equation v^(2) = u^(2)+2 as is dimensionally homogeneous.

If (x+iy)^(3) = u + iv , then show that u/x + v/y = 4(x^(2)-y^(2))

If y = e^u and u = f(x), show that, (d^2y)/(dx^2) = e^u [(d^2u)/(dx^2) + ((du)/(dx))^2] .

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a) 6 real roots b) at least 2 real roots c) 4 real roots d) none of these

The sum of the non-real root of (x^2+x-2)(x^2+x-3)=12 is a. -1 b. 1 c. -6 d. 6

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. 0ltthetaltpi/2, if x=sum(n=0)^inftycos^(2n)theta,y=sum(n=0)^inftysin^(...

    Text Solution

    |

  2. The real numbers x1, x2, x3 satisfying the equation x^3-x^2+b x+gamma=...

    Text Solution

    |

  3. Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system...

    Text Solution

    |

  4. The 5th, 8th and 11th terms of a GP are a,b,c respectively. Show that...

    Text Solution

    |

  5. If (log)3 2,(log)3(2^x-5)a n d(log)3(2^x-7/2) are in arithmetic progre...

    Text Solution

    |

  6. If p be the first of n arithmetic means between two numbers and q be t...

    Text Solution

    |

  7. Find the centre and radius of the circle: (x+5)^2+(y-3)^2=20

    Text Solution

    |

  8. The interior angles of a polygon are in arithmetic progression. The sm...

    Text Solution

    |

  9. If a1,a2,a3,.......an are in AP where a1 gt 0foralli then the value of...

    Text Solution

    |

  10. Does there exist a GP containing 27,8 and 12 as three of its terms ? I...

    Text Solution

    |

  11. Find three numbers a,b,c between 2 & 18 such that; their sum is 25; th...

    Text Solution

    |

  12. The sum of 50 terms of the series 1+2(1+1/(50))+3(1+1/(50))^2+ is giv...

    Text Solution

    |

  13. The sum of 50 terms of the series 3/(1^2)+5/(1^2+2^2)+7/(1^2+2^2+3^2)+...

    Text Solution

    |

  14. Which term of the AP 3,10, 17,... will be 84 more than its 13th term?

    Text Solution

    |

  15. The sum of the series a-(a+d)+(a+2d)-(a+3d)+... up to (2n+1) terms is:...

    Text Solution

    |

  16. If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmet...

    Text Solution

    |

  17. Find the number of multiples of 4 lies between 10 and 250.

    Text Solution

    |

  18. Find the sum 3/(1xx2)xx1/2+4/(2xx3)xx(1/2)^2+5/(3xx4)xx(1/2)^3+ to n t...

    Text Solution

    |

  19. Find the sum of the series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1...

    Text Solution

    |

  20. If k, 2(k+1), 3(k+1) are in GP, Then find the value of k.

    Text Solution

    |