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the question is from the book "elementary geometry from an advanced standpoint 3rd edition" by edwin e. moise

Given x>0 and y>0, show that x^3 = y^3 => x = y. Does this hold for all every x and y?

a^3-b^3=(a-b)(a^2+ab+b^2)=0

so what i did was subtract y^3 from both sides to get

x^3-y^3 = 0

then i factored it out to

(x-y)(x^2+xy+y^2) = 0

because we know that x>0 and y>0, the second term (x^2+xy+y^2) is always positive. because of this (x-y) must equal zero

then we setup the equation x-y=0

x=y.

i think i did this correctly, but since i am teaching myself out of this book (i just want to learn more about geometry because i felt like i was never taught it well) i have no way of verifying if this is correct

## Homework Statement

Given x>0 and y>0, show that x^3 = y^3 => x = y. Does this hold for all every x and y?

## Homework Equations

a^3-b^3=(a-b)(a^2+ab+b^2)=0

## The Attempt at a Solution

so what i did was subtract y^3 from both sides to get

x^3-y^3 = 0

then i factored it out to

(x-y)(x^2+xy+y^2) = 0

because we know that x>0 and y>0, the second term (x^2+xy+y^2) is always positive. because of this (x-y) must equal zero

then we setup the equation x-y=0

x=y.

i think i did this correctly, but since i am teaching myself out of this book (i just want to learn more about geometry because i felt like i was never taught it well) i have no way of verifying if this is correct

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