Question

The difference of two numbers is 5 and the difference of their square is 65. Find both the numbers show all steps

Answer 1

Answer:

let two numbers are α and β. (where α>β)

given, (α-β) = 5 -----------(i)

and, α²-β²= 65

=> (α+β)(α-β)=65

=> (α+β)5 = 65

=> (α+β) = 65/5

=> (α+β) = 13 ----------(ii)

sloving equation (i) and (ii) add both

α-β = 5

α+β = 13

---------------

2α = 18

α = 9

putting the value of α in equation in equation (i)

then, α - β = 5

=> 9 - β = 5

=> β = 4

Hence , the two numbers are 9 and 4.

Answer 2

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

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.

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

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 =5We then expand the binomial inside the parenthesis,

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 =5We then expand the binomial inside the parenthesis,x^2 - (25 - 10x + x^2) = 5 and then remove the parenthesis

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 =5We then expand the binomial inside the parenthesis,x^2 - (25 - 10x + x^2) = 5 and then remove the parenthesisx^2 - 25 + 10x - x^2 = 5 and simplify terms

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 =5We then expand the binomial inside the parenthesis,x^2 - (25 - 10x + x^2) = 5 and then remove the parenthesisx^2 - 25 + 10x - x^2 = 5 and simplify terms-25 + 10x = 5 then add 25 to both sides of the equation

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 =5We then expand the binomial inside the parenthesis,x^2 - (25 - 10x + x^2) = 5 and then remove the parenthesisx^2 - 25 + 10x - x^2 = 5 and simplify terms-25 + 10x = 5 then add 25 to both sides of the equation10x = 30 and multiply both sides by 1/10

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 =5We then expand the binomial inside the parenthesis,x^2 - (25 - 10x + x^2) = 5 and then remove the parenthesisx^2 - 25 + 10x - x^2 = 5 and simplify terms-25 + 10x = 5 then add 25 to both sides of the equation10x = 30 and multiply both sides by 1/10x = 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