Question 22857
x+y=27
y=27-x
xy=152
x(27-x)=152
{{{-x^2+27x=152}}}
{{{-x^2+27x-152=0}}}
Use Quadratic formula: {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
a= -1, b=27, c=-152
{{{x = (-27 +- sqrt( 27^2-4(-1)(-152) ))/2(-1)) }}} 
{{{x = (-27 +- sqrt( 729-608))/-2)}}}
{{{x = (-27 +- sqrt(121))/-2)}}}
Add: {{{x = (-27 + 11/-2)}}}
x=8
27-8 = 19
Hence, the two numbers are 8 and 19.