Home
Class 12
MATHS
Find the least value of ((6x^2-22 x+21))...

Find the least value of `((6x^2-22 x+21))/((5x^2-18x+17))` for real `xdot`

Text Solution

Verified by Experts

Ler `((6x^(2) - 22x +21))/((5x^(2)-18x + 17))`
or `(6-5y)x^(2) -2x (11 - 9y) + 21 - 17y =0`
Since x is real, we have
`4(11-9y)^(2) - 4(6-5y) (21-17y) ge 0`
or `-4y^ + 9y - 5 ge 0`
or `4y^(2)+ 9y - 5 le 0`
or `(y - 1) (4y - 5) le 0`
`rArr ` le y le 5//4`
Hence, the least value of the given expression is 1.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLES|14 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.1|3 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|6 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

IF x is real, find the greatest and the least value of (6x^2-22x-21)/(5x^2-18x+17) , also find the corresponding values of x.

IF x is real , find the greatest and the least value of : (x^2-2x+2)/(x^2+3x+9)

For real x,the least value of (x-2)(x-3)+1 is___

The least value of 2x^(2)+y^(2)+2xy+2x-3y+8 for real numbers x and y is -

IF x is real , find the maximum and minimum values of (x^2-x+1)/(x^2+x+1) also find the corresponding values of x.

Find the least value of sec^6x+cos e c^6x+sec^6xcos e c^6xdot

If x be real , find the greatest value of (x+2)/(2x^2+3x+6) .

Evaluate : lim_(x->2)(x^2-5x+6)/(x^2-4)

Find the value of (x^3 - 7x^2 + 13x + 17) when x = 2 + sqrt3

IF x is real , find the greatest and the least value of : (x^2+14x+9)/(x^2+2x+3)

CENGAGE PUBLICATION-THEORY OF EQUATIONS-ILLUSTRATION
  1. If aa n dc are odd prime numbers and a x 62+b x+c=0 has rational roots...

    Text Solution

    |

  2. Find the range of the fuction f(x) = x^(2) - 2x -4

    Text Solution

    |

  3. Find the least value of ((6x^2-22 x+21))/((5x^2-18x+17)) for real xdot

    Text Solution

    |

  4. Prove that if the equation x^2+9y^2-4x+3=0 is satisfied for real value...

    Text Solution

    |

  5. The least value of the expression x^2+4y^2+3z^2-2x-12 y-6z+14 is 3 b. ...

    Text Solution

    |

  6. Find the linear factors of 2x^2-y^2-x+x y+2y-1.

    Text Solution

    |

  7. If the expression 2x^(2)+mxy+3y^(2)-5y-2 can be resolved into two rati...

    Text Solution

    |

  8. Form a quadratic equation whose roots are -4 and 3.

    Text Solution

    |

  9. Form a quadratic equation with real coefficients whose one root is 3-2...

    Text Solution

    |

  10. If roots of the equation a x^2+b x+c=0 are alpha and beta , find the e...

    Text Solution

    |

  11. If alpha,beta are the roots of lthe equation 2x^2-3x-6=0, find the equ...

    Text Solution

    |

  12. If alpha!=betaa n dalpha^2=5alpha-3a n dbeta^2=5beta-3. find the equat...

    Text Solution

    |

  13. If roots of equation 3x^(2) + 5x + 1 = 0 are (sectheta(1) - tentheta(1...

    Text Solution

    |

  14. If a b+b c+c a=0, then solve a(b-2c)x^2+b(c-2a)x+c(a-2b)=0.

    Text Solution

    |

  15. If a ,b ,a n dc are in A.P. and one root of the equation a x^2+b c+c=0...

    Text Solution

    |

  16. If alpha is a root of the equation x^2+2x-1=0, then prove that 4alpha^...

    Text Solution

    |

  17. If the roots of the equadratic equation x^(2) + px + q = 0 " are " tan...

    Text Solution

    |

  18. The sum of roots of equation 1/(x+a)+1/(x+b)=1/c is zero find the prod...

    Text Solution

    |

  19. Solve the equation x^2+p x+45=0. it is given that the squared differen...

    Text Solution

    |

  20. If alpha,beta are the roots of the equation 2x^2-35x+2=0 , the find th...

    Text Solution

    |