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Solve (x+4)^3 + (x+5)^3 = (x+7)^3 + (x-2)^3

 Apr 12, 2022
 #1
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Simplifying  by the binomial theorem, we get

 

x^3 + 12x^2 + 48x + 64 + x^3 + 15x^2 + 75x +125 = x^3 + 21x^2 + 147x + 343 + x^3 - 6x^2 + 12x - 8 

 

Subtract out the x^3 terms....simplify the rest

 

27x^2  + 123x + 189  =  15x^2 + 159x + 335

 

12x^2 -36x -  146 = 0    divide through by 2

 

6x^2  -18x - 73  = 0

 

Using the Quadratic Formula the two solutions  are  x ≈ -2.2969    or  x ≈ 5.2969

 

 

cool cool cool

 Apr 12, 2022

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