MathematicsThe sum of the squares of two integers is 233 and one integer is 3 less than twice the other integer. Find the numbers.

The sum of the squares of two integers is 233 and one integer is 3 less than twice the other integer. Find the numbers.


  1. A
    8 and 13
  2. B
    8 and 43
  3. C
    6 and 23
  4. D
    7 and 15 

    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:

    Given that the sum of the squares of two integers is 233 and one integer is 3 less than twice the other integer.
    Let the first integer be x and the other integer be 2x-3.
    Now, according to the question, writing the algebraic expression as follows:
    x 2 + 2x3 2 =233  
    x 2 +4 x 2 12x+9=233  
    5 x 2 12x+9233=0  
    5 x 2 12x224=0  
    5 x 2 40x+28x224=0  
    5x x8 +28 x8 =0  
    x8 5x+28 =0 x=8 or x= 28 5  
    Since x is an integer, so x 28 5 .  
    Thus, x=8.
    2x3=2 8 3=13  
    Therefore, the numbers are 8 and 13.
    Hence, option (1) is correct.
     
    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.