Question

The product of two numbers is 750.The sum of their squares is 1525 and the sum of the numbers and their difference will be? ​

Answer 1

The sum of numbers is 55.

The difference of number is 5.

Step-by-step explanation:

Let one number is x and other number is y.

Given:

1. The product of two numbers is 750.
2. The product of two numbers is 750.The sum of their squares is 1525.

So,

$= > \: xy = 750$

$= > \: {x}^{2} + {y}^{2} = 1525$

As we know that,

$= > \: {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

$= > \: {(x + y)}^{2} = 1525 + 2 \times 750$

$= > \: {(x + y)}^{2} = 3025$

$= > \: (x + y) = \sqrt{3025}$

$= > \: (x + y) = 55$

So, the sum of two numbers is 55.

Now,

$= > \: x + \frac{750}{x} = 55$

$= > \: {x}^{2} - 55x + 750 = 0$

$= > \: {x}^{2} - 30x - 25x + 750 = 0$

$= > \: x \times (x - 30) - 25 \times (x - 30) = 0$

$= > \: (x - 25)(x - 30) = 0$

$x = 20 \: and \: x = 30$

If x=20 then y = 55 - 20 =35. But for this value the product of x and y is not equal to 750 . So, x=20 is not be taken.

For x=30 the value of y is 25.

The difference of two number is 5.