Find all the solutions of:

a^3=2b^3+3c^3

if a,b,c are integers

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Notice that for a=b=c=0, the relation `a^3=2b^3+3c^3`  is a mathematical truth.

Since the number are integer, I'll propose you to consider the next possible solution: a=5, b=4 and c=-1.

`5^3 = 2*4^3 + 3*(-1)^3`

125 = 128 - 3

125 = 125

Of course, you can also use the possible solution a=-5,b=-4,c=1

`(-5)^3 = 2*(-4)^3 + 3*(1)^3`

-125 = -128 + 3

-125=-125

ANSWER: The possible solutions of `a^3=2b^3+3c^3`  are a=b=c=0;a=5, b=4 and c=-1; a=-5,b=-4,c=1.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial