Question

The sum of two numbers is 7 and the difference of their squares is 105. Find the numbers. If there

In simplest form.
more than one pair, use the "or" button. Give the answer
In simplest form

Answer 1

11 and -4

Explanation:

Let the required two numbers be x and y

If the sum of two numbers is 7, then

x + y = 7 .. 1

If the difference of their squares is 105, then;

x² - y² = 105 ...2

From 1;

x = 7 - y... 3

Substitute 3 into 2;

(7-y)² - y² = 105

Expand

49-14y+y² -y² = 105

49-14y = 105

-14y = 105 - 49

-14y = 56

y = -56/14

y = -4

Substitute y = -4 into 3

x = 7 - y... 3

x = 7 - (-4)

x = 7+4

x = 11

Hence the numbers are 11 and -4