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find the two numbers whose sum 19 and the product of the difference and the greater, is 60​

Sagot :

Answer:

12 and 7

Step-by-step explanation:

One number is x, and the other number is (19-x).

ikaw na mag compute mahirap itype

Answer:

7 and 12

Solution:

Let x be the greater number and y be the lesser number

[tex]x + y = 19[/tex]

[tex]y = -x +19[/tex]

[tex]x(x-y) = 60[/tex]

Substitute x for y

[tex]x(x-(-x+19)) = 60[/tex]

[tex]2x^2 + 19x = 60[/tex]

Subtract 60 to both sides

[tex]2x^2 + 19x - 60[/tex]

Solve this using quadratic formula where a = 2, b = 19 and c = -60

[tex]x = \frac{-b±\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x = \frac{-19±\sqrt{-19^2-4(2)(-60)} }{2(2)}[/tex]

[tex]x = \frac{-19±\sqrt{841} }{4}[/tex]

[tex]x = 12[/tex]

We will ignore 2.5 because 2.5 doesnt comply the sum of 19

Since we already found x, we can now find y

x + y = 19

12 + y = 19

y = 7

Therefore x = 12 and y = 7

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