If x-y=6 and x^2+y^2=24, find x^3-y^3.

162.06

Step-by-step explanation:

sorry i'm not the best an explaining but i'm confident in my answer.

the first thing to do is get rid of the ² in x²+y²=24, we do this by √24 which ≅4.90 (i rounded to the hundreth place)

then we have this

x-y=6

x+y=4.90

I am using the elmination method. To do that you need to get two letters to have the same coefficient (in 4x 4 is the coefficient) with oposite signs (one possitive one negitive)

In our equation here we see that the same coefficient is 0, and there is oposite signs for y. Therefore we can add the two equations and get

2x=10.9 (the y cancels out)

now we have a simple equation and all that is left is to solve it

10.9/2=5.45

x=5.45

Now we need to find y we do that by pluging the x value into one of the equations I choose the first one becasue its easiest.

(5.45)-y=6  

y= - .55

now that we have both x and y plug them into the final equation (5.45)³-(-.55)³= 161.89-(-.17) =162.06

Therefore x³-y³≅162.06!

(if you have any questions or would like to debate the answer please let me know!)

nlgqer

step-by-step