Home
Class 12
MATHS
Find two number whose sum is 8 and the s...

Find two number whose sum is 8 and the sum of their cubes is minimum.

Text Solution

AI Generated Solution

To find two numbers whose sum is 8 and the sum of their cubes is minimized, we can follow these steps: ### Step 1: Define the Variables Let the two numbers be \( x \) and \( y \). According to the problem, we have: \[ x + y = 8 \] ...
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 6a|20 Videos
  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 6b|17 Videos
  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.

Find two positive numbers whose sum is 14 and the sum of whose squares is minimum.

Find two positive numbers whose sum is 15 and the sum of whose squares is minimum.

Determine two positive numbers whose sum is 15 and the sum of whose squares is minimum.

Find two positive numbers whose sum is 14 and the sum of whose squares in minimum.

Find two number whose sum is 100 and the sum of twice of first part and square of the second is minimum.

Consider two numbers a,b, sum of which is 3 and the sum of their cubes is 7. Then sum of all possible distinct values of a is :

Find two numbers whose sum is 12 and the product of the square of one part and the 4th power of other is maximum.

The sum of two numbers is 7 and the sum of their cubes is 133. Find the sum of their squares

Find three numbers in A.P. whose sum is 9 and sum of whose cubes is 99.

NAGEEN PRAKASHAN ENGLISH-APPLICATIONS OF DERIVATIVES-Miscellaneous Exercise
  1. Find two number whose sum is 8 and the sum of their cubes is minimum.

    Text Solution

    |

  2. Using differentials, find the approximate value of each of the follow...

    Text Solution

    |

  3. Show that the function given by f(x)=(logx)/xhas maximum at x = e.

    Text Solution

    |

  4. The two equal sides of an isosceles triangle with fixed base b are ...

    Text Solution

    |

  5. Find the equation of the normal to the curve x^2=4\ y which passes ...

    Text Solution

    |

  6. Show that the normal at any point theta to the curve x=acostheta+at...

    Text Solution

    |

  7. Find the intervals in which the function f given by f(x)=(4sinx-2x-x c...

    Text Solution

    |

  8. Find the intervals in which the function f given by f(x)=x^3+1/(x^3),\...

    Text Solution

    |

  9. Find the area of the greatest isosceles triangle that can be inscri...

    Text Solution

    |

  10. A tank with rectangular base and rectangular sides, open at the top ...

    Text Solution

    |

  11. The sum of the perimeter of a circle and square is k, where k is so...

    Text Solution

    |

  12. A window is in the form of a rectangle surmounted by a semicircular...

    Text Solution

    |

  13. A point on the hypotenuse of a triangle is at distance a and b from...

    Text Solution

    |

  14. Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 h...

    Text Solution

    |

  15. Find the absolute maximum and minimum values of the function f give...

    Text Solution

    |

  16. Show that the altitude of the right circular cone of maximum volume ...

    Text Solution

    |

  17. Let f be a function defined on [a, b] such that f^(prime)(x)>0, for al...

    Text Solution

    |

  18. Show that the height of the cylinder of maximum volume that can be ...

    Text Solution

    |

  19. Show that height of the cylinder of greatest volume which can be in...

    Text Solution

    |

  20. A cylindrical tank of radius 10 m is being filled with wheat at the r...

    Text Solution

    |

  21. The slope of the tangent to the curve x=t^2+3t-8,y=2t^2-2t-5at the po...

    Text Solution

    |