Question

The sum of the cubes of two numbers is 793. The sum



of the numbers is 13, then the difference of the two



numbers is:

Answer 1

Step-by-step explanation:

The sum of the cubes of two numbers is 793. The sum of the numbers is 13. Then the difference of the two numbers is

1). 7

2). 6

3). 5

4). 8

Answer option 6

Answer 2

Given:

• The sum of the cubes of two numbers is 793. The sum of the numbers is 13.

To Find

• The difference of the two numbers is?

Explanation

Let the two numbers be x and y

so as;

• x³ + y³ = 793
• x + y = 13

Using Quantities,

$\\ \dag{\red{\boxed{\underline{\sf\large{ (x+y)^3 = x^3 + y^3 + 3xy(x+y) }}}}}$

Putting values,

$\colon\implies{\tt{ (x+y)^3 = x^3 + y^3 + 3xy(x+y)}} \\ \\ \\ \colon\implies{\tt{ (13)^3 = 793 + 3xy(13) }} \\ \\ \\ \colon\implies{\tt{ 2197-793 = 3xy(13)}} \\ \\ \\ \colon\implies{\tt{ 1404 = 3xy \times 13 }} \\ \\ \\ \colon\implies{\tt{ 1404 = 39xy }} \\ \\ \\ \colon\implies{\tt{ xy = \dfrac{ \cancel{1404} }{ \cancel{39} } }} \\ \\ \\ \colon\implies{\tt{ xy = 36 }}$

• Value of xy is 36.

Now, We have to find the Sum of the square of the two numbers:-

• x² + y² = ?

$\\ \dag{\pink{\underline{\boxed{\sf\large{ (x+y)^2 = x^2 + y^2 + 2xy }}}}}$

As we know that,

• x + y = 13
• xy = 36

Putting values,

$\colon\implies{\tt{ (x+y)^2 = x^2 + y^2 + 2xy }} \\ \\ \\ \colon\implies{\tt{ (13)^2 = x^2 + y^2 + 2 \times 36 }} \\ \\ \\ \colon\implies{\tt{ 169 = x^2 + y^2 + 72 }} \\ \\ \\ \colon\implies{\tt{ 169 - 72 = x^2 + y^2 }} \\ \\ \\ \colon\implies{\tt{ 97 = x^2 + y^2 }}$

• So, Value of x² + y² is 97

So, Now We can find the value of difference of two numbers as:-

As We know that,

• x² + y² = 97
• xy = 36

We also Know,

$\\ \dag{\purple{\boxed{\underline{\sf\large{ (x-y)^2 = x^2 + y^2 - 2xy }}}}}$

Putting values Properly,

$\colon\implies{\tt{ (x-y)^2 = x^2 + y^2 - 2xy }} \\ \\ \\ \colon\implies{\tt{ (x-y)^2 = 97 - 2 \times 36 }} \\ \\ \\ \colon\implies{\tt{ (x-y)^2 = 97 - 72 }} \\ \\ \\ \colon\implies{\tt{ (x-y)^2 = 25 }} \\ \\ \\ \colon\implies{\tt{ x-y = \sqrt{25} }} \\ \\ \\ \colon\implies{\boxed{\tt\large\orange{ x-y = 5 }}}$

Hence,

• The Value of the difference of two numbers is 5 .