+0

# calculate

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(\root(3)(x+1)-\root(3)(x))((\root(3)(x+1))^(2)+\root(3)(x+1)\root(3)(x)+(\root(3)(x))^(2))

Guest Oct 15, 2017

#1
+5241
+1

³√( x + 1 )  -  ³√( x ) )( ³√( x + 1 )2  +  ³√( x + 1 )³√( x )  +  ³√( x )2 )

Since         (a - b)(a2 + ab + b2)   =   a3 - b3

so does...

³√( x + 1 )  -  ³√( x ) )( ³√( x + 1 )2  +  ³√( x + 1 )³√( x )  +  ³√( x )2 )     =    ³√( x + 1 )3  -  ³√( x )3

=   x + 1  -  x   =   1

hectictar  Oct 15, 2017
Sort:

#1
+5241
+1

³√( x + 1 )  -  ³√( x ) )( ³√( x + 1 )2  +  ³√( x + 1 )³√( x )  +  ³√( x )2 )

Since         (a - b)(a2 + ab + b2)   =   a3 - b3

so does...

³√( x + 1 )  -  ³√( x ) )( ³√( x + 1 )2  +  ³√( x + 1 )³√( x )  +  ³√( x )2 )     =    ³√( x + 1 )3  -  ³√( x )3

=   x + 1  -  x   =   1

hectictar  Oct 15, 2017
#2
+78618
+1

Nice to recognize that it was just a difference of cubes, hectictar.......!!!

CPhill  Oct 15, 2017

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