Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

What 2 numbers are multiplied to get -24 but sums up to +6?

help

Update:

Nevermind 

6 Answers

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  • 1 month ago

    a=3- sqrt(33)

    b=3+sqrt(33)

  • Philip
    Lv 6
    1 month ago

    xy = -24...(1).;

    x+y = 6 ...(2).;

    (1)---> y = -(24/x);

    Then (2)---> x = 6+(24/x);

    Then x^2 = 6x +24, ie., x^2-6x = 24, ie., x^2-6x+9 = 33, ie., (x-3)^3 = (rt33)^2, ie.,;

    x = 3(+/-)rt33;

    corresponding y = 3(-/+)rt33; 

  • David
    Lv 7
    1 month ago

    The numbers needed are: 3 -square root of 33 and 3 +square root of 33

  • Ian H
    Lv 7
    1 month ago

    x + y = 6, and let

    x – y = 2t, so then

    x = 3 + t, and

    y = 3 - t

    We can find t using

    4t^2 = (x – y)^2 = (x + y)^2 – 4xy = 36 + 4*24 = 132

    t^2 = 33, symmetric results for x and y, so select one, say

    x = 3 + √33

    y = 3 - √33

    Check: (3 + √33)(3 - √33) = 9 – 33 = -24 as required.

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  • 1 month ago

    Let the numbers to 'm' & 'n' 

    Hence 

    mn = -24 

    m + n = 6 

     m = -24/n 

    Substitute 

    -24/n + n = 6 

    Multiply through by 'n' 

    -24 + n^2 = 6n 

    n^2 - 6n - 24 = 0 

    It is now in Quadratic form 

    Complete the Square 

    (n - 3)^2 - ( 3)^2 = 24 

    ( n- 3)^2 - 9 = 24 

    (n - 3)^2 = 33 

    Square root both sides 

    n - 3 = +/-sqrt(33)

    n = 3 +/-sqrt(33) 

    n = 3 +/- 5.7445....

    n = - 8 .7445.... or - 2.7445.... 

    Hence m = -24/(-8.7445... ) or -24/-2.7445,]... 

    m = 2.7445... or 8,7445...

    So as pairs of numbers (-8.7445... , 2.7445..) & ( 8.7445... , -2.7445..)

  • 2 months ago

    Two numbers that multiply to -24 and adds to 6:

    xy = -24 and x + y = 6

    x + y = 6

    x = 6 - y

    xy = -24

    (6 - y)y = -24

    6y - y² = -24

    -y² + 6y = -24

    y² - 6y = 24

    y² - 6y + 9 = 24 + 9

    (y - 3)² = 33

    y - 3 = ± √33

    y = 3 ± √33

    We have two y's which will give us two x's, but they will be the same two numbers.

    So your numbers are:

    3 - √33 and 3 + √33

    Testing:

    3 - √33 + 3 + √33

    3 + 3

    6 <-- true

    (3 - √33)(3 + √33)

    9 + 3√33 - 3√33 - 33

    9 - 33

    -24 <-- true

    So those are your numbers.

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