If xy = 144 and x + y = 30, what is the value of x and y?

To find the values of x and y, we can start with the two equations we have:

1. xy = 144
2. x + y = 30

From the second equation, we can express y in terms of x:

y = 30 – x

Now, we can substitute this expression for y into the first equation:

x(30 – x) = 144

Expanding this gives:

30x – x² = 144

Rearranging this into standard quadratic form:

x² – 30x + 144 = 0

Next, we can apply the quadratic formula, which states that for any equation of the form ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b² – 4ac)) / (2a)

Here, a = 1, b = -30, and c = 144:

x = (30 ± √((-30)² – 4(1)(144))) / (2(1))

x = (30 ± √(900 – 576)) / 2

x = (30 ± √324) / 2

x = (30 ± 18) / 2

Calculating the possible values for x:

x = (48) / 2 = 24

or

x = (12) / 2 = 6

Now, we can find y by substituting these values back into the equation y = 30 – x:

If x = 24, then y = 30 – 24 = 6.

If x = 6, then y = 30 – 6 = 24.

Therefore, the pairs (x, y) that satisfy both equations are (24, 6) and (6, 24). In conclusion:

The values of x and y are 24 and 6.