Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Positive real number is four less than another. if the sum of the squares of the two numbers is 72 what are the numbers?

3 Answers

Relevance
  • Amy
    Lv 7
    1 month ago

    Write statement as an equation

    x^2 + (x+4)^2 = 72

    Expand the squared term

    2x^2 + 8x + 16 = 72

    Combine like terms

    2x^2 + 8x - 56 = 0

    Divide all by 2

    x^2 + 4x - 28 = 0

    Plug into quadratic formula

    x = [-4 ± √(4^2 + 4*1*28) ] / [2*1]

    Simplify

    x = -2 ± 4√2

    Only the positive answer is allowed

    x = -2 + 4√2

  • 1 month ago

    Let the numbers be 'n' & n - 4' 

    Squared 

    n = n^2 = n- 4 = ( n-4)^2 

    Hence the sum of their squares is 

    n^2 + ( n- 4)^2 = 72 

    Expand the brackets 

    n^2 + n^2 - 8n + 16 = 72 

    Collect 'like terms' 

    2n^2 - 8n = 56  

    Factor out '2' 

    n^2 - 4n = 28

    This will not factor so 'Complete the Square'. 

    (n - 2)^2 - (-2)^2 = 28 

    ( n- 2)^2 - 4 = 28 

    ( n- 2)^2 = 24 

    Square root both sides 

    n - 2 = 2sqrt(6)

    n = 2 +/-2sqrt(6)

    n = 2 +/- 2.44948.... 

    Hence the two numbers are 

    n = 4.44948... 

    n = 0.44948....

  • 1 month ago

    Letting the numbers be a and b we have:

    a - 4 = b

    i.e. a - b = 4...(1)

    Also, a² + b² = 72...(2)

    Then, (b + 4)² + b² = 72

    so, 2b² + 8b - 56 = 0

    or, b² + 4b - 28 = 0

    Using the quadratic formula yields:

    b = 3.66 or -7.66

    Hence, a = 7.66 or -3.66

    As the numbers are positive and real we have a = 7.66 and b = 3.66

    Note: we see that 3² + 7² = 58

    and 4² + 8² = 80

    so, by inspection we see that a is between 7 and 8, therefore b is between 3 and 4.

    :)>

Still have questions? Get answers by asking now.