Question

The difference of the squares of two numbers is 15. The difference of twice the square of the first number and the square of the second number is 30. Find the numbers

Answer 1

Explanation:

Let x represent the first number, and y be the second number.

The first statement can be modeled as

`{x}^(2) - {y}^(2) = 15`

The second statement can modeled as

`2 {x}^(2) - {y}^(2) = 30`

If we multiply 2 both sides of the first equation,

`2( {x}^(2) - {y}^(2) ) = 15 * 2`

`2 {x}^(2) - 2 {y}^(2) = 30`

Subsitue this for 30 in second equation,

`2 {x}^(2) - {y}^(2) = 2 {x}^(2) - {2y}^(2)`

`{y}^(2) = 0`

`y = 0`

Subsitue this for y in either equation,

`{x}^(2) = 15`So our answer is

plus or minus sqr root of 15, 0).

`(± √(15) ,0)`

`x = √(15)`

or

`x = - √(15)`