Answer: = [tex]\frac{25+\sqrt{949} }{6}[/tex] and y = \frac{25+\sqrt{949} }{6} - 3.
Step-by-step explanation:
Take x as the larger number and y as the smaller number.
x + 3 = y
[tex]\frac{16}{y}[/tex]+ [tex]\frac{9}{x}[/tex] = 1
Substitute x + 3 for y in the second equation.
[tex]\frac{16}{x+3}[/tex]+ [tex]\frac{9}{x}[/tex] = 1
Make a common denominator.
[tex]\frac{16(x) + 9(x+3)}{(x+3)(x)} =1[/tex]
Simplify and get rid of that fraction.
[tex]16x + 9x + 27 = x^{2} + 3x[/tex]
[tex]x^{2} + 3x - 25x - 27 = 0[/tex]
[tex]x^{2} -22x - 27 = 0[/tex]
By quadratic formula (and because they must be positive), x = [tex]\frac{25+\sqrt{949} }{6}[/tex] and then y = \frac{25+\sqrt{949} }{6} - 3.
