Question

The sum of two numbers is 15 and sum of their squares is 113. find the numbers.

Answer 1

Let the numbers be x and (15 - x).
Then,x2+(15−x)2=113?

=> x2+225+x2−30x=113

=> 2x2−30x+112=0

=> x2−15x+56=0

=> (x - 7) (x - 8) = 0

=> x = 7 or x = 8.

So, the numbers are 7 and 8.

Answer 2

The two numbers are 7 and 8.      

Step-by-step explanation:

We are given that the sum of two numbers is 15 and the sum of their squares is 113.

Let the one number be x and another number be y.

• The first condition states that the sum of two numbers is 15, that is;

                              x + y = 15  

                               y = 15 - x  ---------------- [Equation 1]

• The second condition states that the sum of their squares is 113, that is;

                             $x^{2} +y^{2} =113$

                             $x^{2} +(15-x)^{2} =113$       {using equation 1}

                             $x^{2} +15^{2} +x^{2} -2(15)(x) =113$

                             $2x^{2} -30x+225 - 113 =0$

                             $2x^{2} -30x+112 =0$

                             $x^{2} -15x+56 =0$

Now, using middle term splitting method to solve the above expression;

                             $x^{2} -7x-8x+56 =0$

                             $x(x -7)-8(x-7) =0$

                             $(x-7)(x-8)=0$

So, either x - 7 = 0  or   x - 8 = 0

                x = 7 or x = 8.

Now, if x = 7, then y = 8 and if x = 8. then y = 7

Hence, the two numbers are 7 and 8.