Mathematics Three consecutive positive integers are such that the square of their sum exceeds the sum of their squares by 214. Which are those three integers?

 Three consecutive positive integers are such that the square of their sum exceeds the sum of their squares by 214. Which are those three integers?


  1. A
    6,7,8
  2. B
    4,5,6
  3. C
    7,8,9
  4. D
    5,6,7 

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    Let the three consecutive positive integers be x, x+1 and x+2.
    Given, x2+(x+1)2+(x+2)2= (x+x+1+x+2)2−214
    x2+x2+1+2x+x2+4+4x=(3x+3)2−214
    ⇒3x2+6x+5=9x2+9+18x−214
    ⇒3x2+6x+5=9x2+18x−205
    ⇒6x2+12x−210=0
    x2+2x−35=0
    x2+7x−5x−35=0
    ⇒x(x+7)−5(x+7)=0
    ⇒(x+7)(x−5)=0
    Then, x+7=0 or x−5=0
    ⇒x=−7 or x=5
    Given that the numbers are positive.
    Hence, x cannot be −7
    Then, x=5
    So, x+1=5+1=6
    and x+2=5+2=7
    then, The three consecutive positive integers are 5, 6 and 7. Hence (4) is the correct option.
     
    Chat on WhatsApp Call Infinity Learn

      Talk to our academic expert!



      +91


      Live ClassesBooksTest SeriesSelf Learning




      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.