what numbers fit this equation? a3 + b3 = c3..10 points to best answer please help!?

Question

my dad said he would give me £100 if i could tell him what numbers fit into this equation: a3+b3=c3
also if this cant be done please explain why! thanks:D
(10 points to best answer)

Answer 1

Keep all the numbers as zero

Keep a=c and b = 0 or b= c and a=0

I dont think there are any other solutions for a,b,c > 2 according to fermats theorem....

Answer 2

These are not written as exponents and so the equation can be written as 3a + 3b =3c

If 3a + 3b = 3c then 3(a+b) = 3c; divide each side by 3 to give a+b = c.



So any combination that satisfies the equation a+b = c will fit the equation.



Check a=1: b=2: c=3 for 3a + 3b = 3c

(3x1)+(3x2) = 9; 3x3 =9



Check a=7; b=19; c=26 for 3a + 3b = 3c

(3x7)+(3x19) = 78; 3x26 = 78



It always works for any values of a,b and c that satisfy the condition that a+b = c



If the equation is meant to be written as exponents i.e. a^3 + b^3 = c^3 then it has no solutions. This is Fermat's last theorem, one of the most difficult and long lasting problems in mathematics which has only relatively recently been proved.

Formally stated:-

a^n + b^n = c^n has no solutions for n>2

For n = 1 the solutions are obvious (a=1; b=2, c=3 etc. etc.)

For n=2 this is Pythagoras' Theorem, one solution of which is a=3, b=4,c=5)

There are no solutions for n=3 or for any values of n greater than 3

Answer 3

I presume that the 3's are exponents, and a, b and c must be positive integers.

So you are looking for a cube that's equal to the sum of two other cubes.



If the exponent were 2, these would be "Pythagorean Triples," which could represent the 3 sides of a right triangle.



Finding solutions (or a proof that there aren't any), for exponents 3 or greater is known as "Fermat's Last Problem" because he claimed to have a clever proof that there were no solutions. Today, mathematicians believe that he did NOT in fact have a proof. An extremely long proof using very advanced techniques finally did prove that there are no solutions. Wikipedia says "It is among the most famous theorems in the history of mathematics and prior to its 1995 proof was in the Guinness Book of World Records for "most difficult mathematical problems".



You dad is safe.



You can get back at him. Offer HIM something valuable if he can draw the following diagram with one continuous line, without lifting the pencil from the paper or retracing a line. This can't be done (consider where you would have to start and end--each vertex has 5 lines coming into it, but you can only start and stop at 2 vertices, so this takes two lines.)



http://i276.photobucket.com/albums/kk2/freond1/drawproblem.png



It's a square, with both diagonals drawn in, and with an arc between adjacent vertices. I.e., a square inscribed in a circle, with diagonals too.

You can find more info at http://en.wikipedia.org/wiki/Fermat%27s_last_theorem

Answer 4

this is a little trap...!

a^3 + b^3 = c^3

has only no solution

except, of course a = b = c = 0.

This is a particular case of

the theorem of Fermat

which remained unproved

for centuries.

The prove has been established

by a British mathematician just

some years ago!



Your dad did not take much of a risk

to loose £100.

Answer 5

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two

Answer 6

do you mean a^3 +b^3 =c^3 ?



if yes then



what you need to find out is what number a cubed + b cubed = the cube route of c cubed

(or in other words = c)

5^3 + 7^3 = cube route of 471

125 + 346 = 471



cube rt (471) = 7.78049036148



therefore if the number 5 =a then 7=b and 7.78049036148 would equal c





hope i helped

Answer 7

A) 35 because of the fact one hundred% is all or an entire B)0.35 C)80x9=720 so like a million/9 of 720 is 80 D)70x8=560 so approximately 0.12 of 560 is 70 E)840 and the full volume of 8th graders is a million,050 F)50 s x 40 =2000 so 200cmx40= 8000 solid success!!!