Answer
Find out the solution to the system of equations .
To prove
As the equations are
y = x – 10 , 4 = 2xy
[tex]Put\ y = \frac{4}{2x}[/tex]
in the equation y = x – 10
[tex]\frac{4}{2x} = x - 10[/tex]
Than the equation becomes
2x² - 20x - 4 = 0
Taking 2 as common
x² - 10x - 2 = 0
Now using the discriment formula
[tex]D = -b\pm \frac{\sqrt{b^{2} - 4ac}}{2a}[/tex]
Here a = 1 , b = -10 , c = -2
Put in the above
[tex]x = 10\pm \frac{\sqrt{(-10)^{2} - 4\times 1\times -2}}{2}[/tex]
[tex]x = 10\pm \frac{\sqrt{100+ 8}}{2}[/tex]
[tex]x = 5\pm \frac{\sqrt{108}}{2}[/tex]
[tex]x = 5\pm \frac{6\sqrt{3}}{2}[/tex]
[tex]x = 5\pm 3\sqrt{3}[/tex]
Thus the solution are
[tex]x = 5\ + 3\sqrt{3}[/tex]
Put in the 4 = 2xy
[tex]y = \frac{4}{2(5+3\sqrt{3} )}[/tex]
[tex]y = \frac{2}{(5+3\sqrt{3} )}[/tex]
When
[tex]x = 5\ - 3\sqrt{3}[/tex]
Put in the 4 = 2xy
[tex]y = \frac{4}{2(5 -3\sqrt{3} )}[/tex]
[tex]y = \frac{2}{(5 - 3\sqrt{3} )}[/tex]
Answer:
C is the answer
Step-by-step explanation:
I took the test on edge 2021
