Question

The sum of two integers equals twelve, while their product equals thirty-five. Which two numbers are they?

Answer 1

Answer: 5 and 7

Explanation:

Given

Sum of the integers is 12

Product of the integers is 35

Suppose the integers are
`x` and
`y`

`\Rightarrow x+y=12\\\\\Rightarrow y=12-x\\\Rightarrow xy=35\\\text{Substitute y}\\\Rightarrow x(12-x)=35\\\Rightarrow 12x-x^2=35\\\Rightarrow x^2-12x+35=0\\\Rightarrow x^2-7x-5x+35=0\\\Rightarrow (x-7)(x-5)=0\\\Rightarrow x=5\ or\ 7`

`\therefore \text{y can be }7\ or\ 5`

Hence, the numbers are 5 and 7.