Online Course Discussion Forum

1.13 MC III Geometry

 
 
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1.13 MC III Geometry
by Tina Jin - Wednesday, 24 January 2024, 8:20 PM
 

Hello,

In the solutions at the back of the book, it says "x^3(abc)=y^3(abc), thus x=y, and then a=b=c." But how is this true? I can have a≠b≠c, for example, 2, 3, 4, and x^3*24=y^3*24, and this is true for all x=y. There is no need for a=b=c right?

Thanks,

Tina Jin

 
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Re: 1.13 MC III Geometry
by Dr. Kevin Wang - Thursday, 25 January 2024, 3:58 PM
 

In the solution, the equation $x^3\cdot abc = y^3\cdot abc$ is derived from the equations $xc = yb$, $xa=yc$, and $xb=ya$.  Since we get $x=y$, then from those equations, $a$, $b$, and $c$ must all be equal.

Picture of Tina Jin
Re: 1.13 MC III Geometry
by Tina Jin - Monday, 29 January 2024, 7:23 AM
 
Thank you! I forgot to plug it back into the equation.