Answer
Find out the solution to the system of equations .
To prove
As the equations are
y = x – 10 , 4 = 2xy
\(Put\ y = \frac{4}{2x}\)
in the equation y = x – 10
\(\frac{4}{2x} = x - 10\)
Than the equation becomes
2x² - 20x - 4 = 0
Taking 2 as common
x² - 10x - 2 = 0
Now using the discriment formula
\(D = -b\pm \frac{\sqrt{b^{2} - 4ac}}{2a}\)
Here a = 1 , b = -10 , c = -2
Put in the above
\(x = 10\pm \frac{\sqrt{(-10)^{2} - 4\times 1\times -2}}{2}\)
\(x = 10\pm \frac{\sqrt{100+ 8}}{2}\)
\(x = 5\pm \frac{\sqrt{108}}{2}\)
\(x = 5\pm \frac{6\sqrt{3}}{2}\)
\(x = 5\pm 3\sqrt{3}\)
Thus the solution are
\(x = 5\ + 3\sqrt{3}\)
Put in the 4 = 2xy
\(y = \frac{4}{2(5+3\sqrt{3} )}\)
\(y = \frac{2}{(5+3\sqrt{3} )}\)
When
\(x = 5\ - 3\sqrt{3}\)
Put in the 4 = 2xy
\(y = \frac{4}{2(5 -3\sqrt{3} )}\)
\(y = \frac{2}{(5 - 3\sqrt{3} )}\)
