Home
Class 12
MATHS
For real numbers x and y, let M be the m...

For real numbers x and y, let M be the maximum value of expression `x^4y + x^3y + x^2 y + x y + xy^2 + xy^3 + xy^4` , subject to `x + y = 3`. Find [M] where [.] = G.I.F.

Text Solution

Verified by Experts

The correct Answer is:
36
Promotional Banner

Topper's Solved these Questions

  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos
  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-1 (PART -II: RMO) |9 Videos
  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos
  • FUNDAMENTAL OF MATHEMATICS

    RESONANCE ENGLISH|Exercise Exercise|135 Videos

Similar Questions

Explore conceptually related problems

The maximum value of xy subject to x +y=8 is :

Find the minimum and maximum values of y in 4x^2 + 12xy + 10y^2-4y + 3 = 0

Let x,y in R , then find the maximum and minimum values of expression (x^(2)+y^(2))/(x^(2)+xy+4y^(2)) .

Find the values of x and y , if (3y -2) + (5 -4x)i=0 , where , x y in R.

Find the real numbers (x,y) that satisfy the equation: xy^(2) = 15x^(2) +17xy + 15y^(2) x^(2)y = 20x^(2) + 3y^(2)

Find f(x, y) if f(x + 2y, 2x + y) = 2xy.

If x- y = 7 and x^(3) - y^(3) = 133. find : xy

If 3x -4y =5 and xy=3 , find : 27x^3 - 64y^3 .

Solve: 3 (2x+ y ) = 7xy 3(x+ 3y ) = 11xy , x ne 0 , y ne 0

RESONANCE ENGLISH-EQUATIONS -EXERCISE-2 (PART-I: PREVIOUS ASKED QUESTION FOR PRE RMO)
  1. What is the smallest possible natural number 'n' for which the equatio...

    Text Solution

    |

  2. Natural numbers k,l,p and q are such that if a and b are roots of x^(2...

    Text Solution

    |

  3. If real numbers a, b, c, d, e satisfy a+1=b + 2 = c+ 3 = d + 4 = e + 5...

    Text Solution

    |

  4. The equations x^2 - 4x + k = 0 and x^2 + kx -4 = 0 where k is a real n...

    Text Solution

    |

  5. Let a, b and c be real numbers such that a - 7b + 8c = 4 and 8a + 4b -...

    Text Solution

    |

  6. Let a, b and c be such that a + b + c= 0 and P=a^(2)/(2a^(2)+ bc) + b^...

    Text Solution

    |

  7. Suppose x^(2)-x +1 is factor of 2x^(6) - x^(5) + ax^(4) + x^(3)+bx^(2)...

    Text Solution

    |

  8. For how many pairs of odd positive integers (a, b), both a, b less tha...

    Text Solution

    |

  9. Find the sum of all those integers n for which n^2+20n+15 is the squar...

    Text Solution

    |

  10. Let a and p be the roots of equation x^2 + x - 3 = 0. Find the value o...

    Text Solution

    |

  11. For real numbers x and y, let M be the maximum value of expression x^4...

    Text Solution

    |

  12. Between 5pm and 6pm, I looked at my watch mistaking the hour hand for ...

    Text Solution

    |

  13. Suppose a, b are positive real numbers such that asqrt(a) + b sqrt(b) ...

    Text Solution

    |

  14. Let a, b be integers such that all the roots of the equation (x^2 + ax...

    Text Solution

    |

  15. In a class, the total numbers of boys and girls are in the ratio 4 : 3...

    Text Solution

    |

  16. If the real numbers x, y, z are such that x^2 + 4y^2 + 16z^2 = 48 and ...

    Text Solution

    |

  17. Suppose 1,2,3 are the roots of the equation x^4 + ax^2 + bx + c = 0. ...

    Text Solution

    |

  18. Determine the sum of all possible positive integers n, the product of ...

    Text Solution

    |

  19. Suppose a, b are integers and a + b is a root of x^2 + ax + b = 0. Wha...

    Text Solution

    |

  20. Integers a, b, c satisfy a + b - c = 1 and a^2 + b^2 - c^2 = -1. What ...

    Text Solution

    |