Question 1065269: Find values of a and b such that
a^2 + 44 = b^3
Daughter's homework and I haven't got the foggiest.
I'm thinking value b would be a multiple of 3 as it is cubed. So I'm looking for a multiple of 3 bigger than 44 with a squared value added to it?
My thinking may be way off but if you could throw some light on it I'd be very grateful.
Thanks
Dan
Found 2 solutions by rothauserc, Boreal:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! b^3 = a^2 + 44
:
take cube root of both sides of =
:
b = (a^2 + 44)^(1/3)
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the integer solution for this is
:
a = + or - 9 and b = 5
:
Answer by Boreal(15235)  (Show Source):
You can put this solution on YOUR website! There are multiple solutions, but the integer one will be a=9 and b=5
I want a perfect square + 44 to equal a perfect cube.
I can start with known perfect cubes, 1,8,27,125,216,343,512, and subtract 44 from them:-43,-36,-17,81,172,299,468.
The first three don't have real number squares, but the fourth is a perfect square, 9, and its square + 44=125, which is 5^3.
For 216, a^2= sqrt (172), and a^2+44=6^3.
For 10^2=100, b^3=144 and b= cube root of 144.
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