Question

If the sum of two numbers is 25 and their multiplication is 100 find its difference​

Answer 1

To find : difference between numbers .

Given : sum of two numbers is 25 their multiplication is 100 .

Solution :  

• Let , two numbers be $x$ and $y$ .
• According to given data we know that sum of two numbers is 25 their multiplication is 100 .
• We represent given conditions as ,

1. $x + y = 25$
2. $xy = 100$

• We know that , $(x+ y ) ^{2} = x^{2}+ 2xy + y^{2}$
• Therefore , substituting the values we solve further .

         $25^{2} = x^{2} + 2(100) + y^{2} \\x^{2} + y^{2} =625 - 200 \\x^{2} +y^{2} = 425$ ----------------(i)$(a - b)^{2} = 425 - 2 (100 )$

• Now applying identity, $(a-b)^{2}=a^{2}+b^{2}-2 a b$

• Substituting the value we get ,  

         $(a - b)^{2} = 425 - 2 (100 )$   ---------------------( from i)

                     $= 425 - 200 \\= 225$

• Taking square root on both sides , we get ,

             $a - b = 15$

Hence ,  difference between numbers is $15$ .