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X+y=2 and x^3 + y^3=56

find x and y

User Selvaram G
by
7.9k points

1 Answer

5 votes

Answer:

To solve for x and y, we can use algebraic manipulation and substitution. Here are the steps:

Rearrange the first equation to solve for y in terms of x:

y = 2 - x

Substitute this expression for y into the second equation, and simplify:

x^3 + (2-x)^3 = 56

x^3 + 8 - 12x + 6x^2 - 3x^3 = 56

-2x^3 + 6x^2 - 12x + 8 = 0

Divide both sides by -2 to simplify the equation:

x^3 - 3x^2 + 6x - 4 = 0

Try to find a root of the equation using synthetic division or guess and check. One possible root is x = 2. Substituting this back into the first equation gives:

2 + y = 2

y = 0

So the solution is x=2 and y=0.

Therefore, the solution to the system of equations is x = 2 and y = 0.

User Fazia
by
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