Question

The sum of the number is 12 and their product is 35 .find the number

Answer 1

Step-by-step explanation:

let one no. is x

other is 12-x

total=12

x(12-x)=35

12x-x^2=35

-x^2+12x=35

x^2-12x+35=0

x^2-7x-5x+35=0

x(x-7)-5(x-7)=0

(x-7)(x-5)=0

x=7,5

Answer 2

Answer:

Numbers will be 7 , 5 or 5 , 7

Step-by-step explanation:

If we have two numbers x and y,

sum of two numbers = x + y =12 (Given)

product of two numbers = x * y = 35 (Given).

So we know

                x * y = 35

            => y = 35 / x -----equation(i)

We also know that

               x + y = 12

           => x = 12 - y

           => x = 12 - 35 / x (putting the value of y from equation(i)

           => x + 35 / x = 12

           => ($x^{2}$ + 35) / x = 12

           => $x^{2}$ - 12x + 35 = 0

           => $x^{2}$ -(7+5)x + 35 = 0

           => x(x - 7) - 5(x - 7) = 0

           => (x - 7) (x-5) = 0

            => x - 7 = 0     and   => x - 5 = 0

            =>x = 7                       => x = 5

when x = 7                                      when x = 5

        y = 35 / 7 = -5                    y = 35/5 = 7

So numbers will 7 , 5 or 5 , 7 (Ans)