There are two numbers that have a difference of 8. When the squares of the numbers are added together, the result is 424. What is the largest...

Let the two numbers be x and y.

Let `x>y` .

According to the given data;

`x-y = 8` -----(1)

`x^2+y^2 = 424` ------(2)

From (1) y = x-8

Use the value of y = x-8 for (2)

`x^2+(x-8)^2 = 424`

`x^2+x^2-16x+64 = 424`

`2x^2-16x-360`

Divide whole term by 2 to make the expression more simple.

`x^2-8x-180 = 0`

`x^2-18x+10x-180 = 0`

`x(x-18)+10(x-18) = 0`

`(x-18)(x+10) = 0`

`x = 18` or `x = -10`

So the Largest number would be 18 or -10. If we consider the numbers to be positive then the answer would be 18.

Comments

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