Question

Two numbers are such that their sum is 10 and the difference of their squares is 20. Find the
numbers​

Answer 1

6*6=36
4*4=16

36-16=20
6+4=10

Answer 2

Answer:

The two numbers whose sum is 10 and difference between whose squares is 20 are 6 and 4.

Step-by-step explanation:

Let the two numbers be a and b and a > b.

It is given that sum of a and b is 10. That is,

a + b = 10.

Let the above equation be equation 1.

It is also given that the difference of their squares is 20. That is,

a² - b² = 20.

Let the above equation be equation 2.

Now,

a² - b² = (a + b) (a - b)

Substituting the values of a² - b² and a + b from equations 2 and 1 respectively, we get

20 = 10 (a - b)

∴ (a - b) = 20 ÷ 10 = 2.

⇒ a - b = 2.

Now let the above equation be equation 3.

We have

a + b = 10

a  - b = 2

Adding these two equations, we get

2 a = 12

⇒ a = 6.

Putting this value of a in equation 1, we get,

6 + b = 10

⇒ b = 10 - 6 = 4.

Hence the values of a and b are 6 and 4 respectively.