Find two integers whose sum is 16 and product is 55

1.	Find two integers whose sum is 16 and product is 55
Answer» Since the sum of the two numbers is 16, let ONE AMONG them be $\sf{x}$ , so that the other will be $\sf{16-x.}$ Given that their product is 55. Then, $\longrightarrow\sf{x(16-x)=55}$ $\longrightarrow\sf{16x-x^2=55}$ $\longrightarrow\sf{x^2-16x+55=0}$ $\longrightarrow\sf{x^2-11x-5x+55=0}$ $\longrightarrow\sf{x(x-11)-5(x-11)=0}$ $\longrightarrow\sf{(x-11)(x-5)=0}$ $\Longrightarrow\sf{x=11\quad OR\quad x=5}$ If $\sf{x=11,}$ then the other number will be $\sf{16-11=5.}$ If $\sf{x=5,}$ then the other number will be $\sf{16-5=11.}$ However, $\bf{11}$ and $\bf{5}$ are the numbers.

Answer»

Since the sum of the two numbers is 16, let ONE AMONG them be $\sf{x}$ , so that the other will be $\sf{16-x.}$