Question

the sum of two positive numbers x and y is 50 and difference of their square is 720. find the numbers

Answer 1

x+y=50
And
x^2 - y^2 =720
(x-y)(x+y)=720
x-y=14.4
Solving both equation
50-y-y=14.4
-2y=-35. 6

y=17.8
x=32.2

Answer 2

Answer:

The numbers are 32.2 and 17.8 .

Step-by-step explanation:

As given

The sum of two positive numbers x and y is 50 and difference of their square is 720.

Than the equation becomes

x + y = 50

x ² - y² = 720

(By using the formula x² - y² = (x - y)(x + y))

(x - y)(x + y) = 720

( As x + y = 50 )

$(x - y) = \frac{720}{50}$

x - y = 14.4

Than the two equations are

x + y = 50

x - y = 14.4

Add the x + y = 50  and x - y = 14.4 .

2x = 50 + 14.4

2x = 64.4

$x =\frac{64.4}{2}$

x = 32.2

Put in the equation  x + y = 50 .

32.2 + y = 50

y = 50 - 32.2

y = 17.8

Therefore the numbers are 32.2 and 17.8 .