Respuesta :
Answer:
x = 13.35, y = - 1.35
or, x = 1.35, y = - 13.35
or, x = - 13.35, y = 1.35
Step-by-step explanation:
Let us assume that x and y are the two numbers.
So, given that (x + y)² = 144
⇒ x² + 2xy + y² = 144 ........ (1)
⇒ x + y = ± 12 ......... (2)
Again, x² + y² = 180 ........... (3)
Now, from equations (1) and (3) we can write 2xy + 180 = 144
⇒ 2xy = - 36
⇒ xy = - 18 ........ (4)
Now, for x + y = 12
⇒ [tex]x - \frac{18}{x} = 12[/tex]
⇒ x² - 18 = 12x
⇒ x² - 12x - 18 = 0
Using the quadratic formula
[tex]x = \frac{12 \pm \sqrt{(-12)^{2} - 4(1)(-18) } }{2}[/tex]
⇒ [tex]x = \frac{12 \pm 14.7}{2} = 13.35, 1.35[/tex]
Now, for x = 13.35, from equation (4) we get, y = - 1.35
And for x = 1.35, from equation (4) we get, y = - 13.35
Now, for x + y = - 12
⇒ x² + 12x - 18 = 0
Using the quadratic formula,
[tex]x = \frac{- 12 \pm \sqrt{12^{2} - 4(1)(-18)}}{2}[/tex]
⇒ [tex]x = \frac{- 12 \pm 14.7}{2} = 1.34, -13.35[/tex]
Now, for x = - 13.35, from equation (4) we get, y = 1.35
And for x = 1.35, from equation (4) we get, y = - 13.35
Therefore, x = 13.35, y = - 1.35
or, x = 1.35, y = - 13.35
or, x = - 13.35, y = 1.35 (Answer)
