what mulitplies to get 121 but adds to get 11/2

Let the two numbers be  x  and  y.

Then, we have:         x · y  =  121          and         x + y  = 3/2

Since:  xy  =  121,  then, solving for x:  y  =  121 / x

Substituting this value of  x  into the equation  x + y  =  3 /2 ,  we get:   x + 121/x  =  3/2.

Multiplying both sides of this equation by  x:  x² + 121  =  3/2x

Multiplying both sides by 2:  2x² + 242  =  3x

Rewriting into quadratic form:  2x² - 3x + 242  =  0

Using the quadratic formual with  a = 2,  b = -3,  and c = 242,  we get:  ( 3 ± √( 9 - 4(2)(242) ) ) / 4

These two answers are:  ( 3 + √(-1927) ) / 4    and    ( 3 - √(-1927) ) / 4

which become the two possible values for  x  and  y.