Math, asked by iiipop, 1 day ago

two numbers differ by 5 and the sum of their squares is 17. Find the numbers

Answers

Answered by SARXASTIC
3

Hi,

Here is your answer

Let the two positive whole numbers be x and y.

Given that these numbers differ by = 5

Therefore x - y = 5 

x = 5 + y

Also given that the sum of their squares = 193

Therefore

x² + y² = 193

Substituting the value of x

(5 + y)² + y² = 193

25 + y² + 10y + y ² = 193

2y² + 10y - 168 = 0

y² + 5y - 84 = 0

y² + 12y - 7y - 84 = 0

y(y + 12) - 7(y + 12)

(y + 12) (y - 7) = 0

y = -12 or y = 7

Rejecting y = -12 as given they are positive whole numbers.

Therefore y = 7

x - 7 = 5

x = 12

The two numbers are 12 and 7.

Hope this helps you.

Answered by MissIncredible34
2

Step-by-step explanation:

The sum of two numbers is 5 and the difference of their squares is 5. How would one find the difference between the numbers?

This test how well we can use algebra to find the values of 2 unknown numbers.

Let x = the first number greater than the second number. Let y be the second number.

The equations are: First for the numbers sum. x + y = 5 and next for the difference of their squares. x^2 - y^2 = 5.

We then write y in terms of x based on the first equation. y = 5 - x. We then substitute y in the second equation. x^2 - (5 - x)^2 =5

We then expand the binomial inside the parenthesis,

x^2 - (25 - 10x + x^2) = 5 and then remove the parenthesis

x^2 - 25 + 10x - x^2 = 5 and simplify terms

-25 + 10x = 5 then add 25 to both sides of the equation

10x = 30 and multiply both sides by 1/10

x = 3 and returning to x + y = 5 the value of y = 2 so the difference between the two numbers is 3 - 2 which simplifies to 1

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