find 2 numbers whose sum is 49 and whose product is 468.

Question

 find 2 numbers whose sum is 49 and whose product is 468

Answer 1

Hi Tracey,

 

Let the two numbers be x and y

 

the sum of two numbers is 49

 

x+y = 49   equation 1

 

The product of two numbers is 468

 

xy=468

x=468/y

 

substitute the value of x in equation 1

 

(468/y)+y = 49

 

(468+y²)/y = 49

 

468+y²=49y

 

y²-49y+468=0

y²-13y-36y+468=0

 

y(y-13)-36(y-13)=0

 

(y-36)(y-13)=0

 

y-36=0  or   y-13=0

y=36   y=13

 

when y=36

x=468/y=468/36=13

 

when y=13

x=468/y=468/13=36

 

so either way the numbers are 13 and 36

Answer 2

 The answer to this question lies in a quadratic equation of:

 

    X^2 - 49 X + 468        those 2 numbers should be the zeros of quadratic.

 

   To find those 2 numbers  Have to write 468 as product of its factors, the 2 factors whose sum 49 and product is 468 is the answer.

   468 = 2 * 234 = 4 * 117 = 12 * 39 = 36 *13

 

      We see that 36 +13 = 49 is the answer.

   

      Going back to our quadratic:

    

      We see that Our quadratic can be factored into:

 

        X^2 - 49 X + 468 = ( X - 36) ( X -12)

 

     So, this problem is standard way of factoring the quadratic , and ultimately calculating its roots.

Answer 3

Hi Tracey;

468/2=234....wrong

468/3=156....wrong

468/4=117....wrong

468/5...........wrong

468/6=78.....wrong

468/7...........wrong

468/8...........wrong

468/9=52.....wrong

468/10.........wrong

468/11.........wrong

468/12=39...wrong

468/13=36.....13+36=49