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Cierra Castillo 2022-07-02 Answered
If x - y = 3 then x 3 - y 3 = ?
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Answers (2)

Dalton Lester
Answered 2022-07-03 Author has 12 answers
Step 1
We know that in general
XXX ( x 3 - y 3 ) = ( x - y ) ( x 2 + x y + y 2 )
and since
XXX x - y = 3
this gives us
XXX ( x 3 - y 3 ) = 3 ( x 2 + x y + y 2 )
There is no single solution.
The table below shows some of the possible combinations:
Given   x y = 3 In which case if   x = then   y = x 3 y 3 = 3 6 189 2 5 117 1 4 63 0 3 27 1 2 9 2 1 9 3 0 27 4 1 63 5 2 117 6 3 189
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Janessa Olson
Answered 2022-07-04 Author has 2 answers
Step 1
From equation (1) y = x - 3
Substitution in (2) gives
3) x 3 - ( x - 3 ) 3 = ?
Consider just the ( x - 3 ) 3
( x - 3 ) ( x - 3 ) ( x - 3 )
( x - 3 ) ( x 2 - 6 x + 9 )
x 3 - 9 x 2 + 27 x - 27
Substituting back into (3)
x 3 - ( x 3 - 9 x 2 + 27 x - 27 )
9 x 2 - 27 x + 27
Set this to equal y
y = 9 x 2 - 27 x + 27
Factor out the 9
4) y = 9 ( x 2 - 3 x + 3 )
Step 2
From this point on it depends what you wish to do with it
Determine the vertex
Consider the - 3 x in equation (4)
Apply ( - 1 2 ) × - 3 = + 3 2
x vertex = + 3 2
By substitution in (4)
y vertex = 9 [ ( 3 2 ) 2 - 3 ( 3 2 ) + 3 ] = 9 [ 3 4 ] = 27 4
Vertex ( x , y ) ( 3 2 , 27 4 )
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