Question

The difference of two numbers is 11 and their product is 42.find these numbers.

Answer 1

$a-b=11\\ a=11+b \\ ab=42 \\(11+b)*b=42 \\ b^2+11b=42 \\ b^2+11b-42=0 \\ b^2 +14b-3b -42=0 \\ b(b+14)-3(b+14)=0 \\ (b+14)(b-3)=0 \\ b+14=0 \ b-3=0 \\b= -14 \ b=3$ $a=11+b \\ 1)a=11-14 \\a=-3 \\ 2)a=11+3 \\ a=14$

Answer 2

$\left\{\begin{array}{ccc}x-y=11&\to x=y+11\\x\cdot y=42\end{array}\right\\\\(y+11)y=42\\y^2+11y-42=0\\y^2+14y-3y-42=0\\y(y+14)-3(y+14)=0\\(y+14)(y-3)=0\iff y=-14\ \vee\ y=3\\\\x=-14+11=-3\ \vee\ x=3+11=14\\\\Answer:-3\ and\ -14\ or\ 14\ and\ 3$