You don't say what kind of numbers they are ,
e.g. if they are rationals
a=1
b = .5
c= 1.1
d= 1.4
sum of squares of those 4 = 4.42
then the 5th number is √.58
if they are integers, they must be
±1,±1,±1,±1,±1 or ±2,±1,0,0,0
e.g. 2^2 + 1^2 + 0^2 + 0^2 = 5
The sum of cubes of the first set is 5
the sum of cubes of the second set is 9
so the numbers must be 2, 1, 0, 0, 0
incidentally the sum of cubes of my first example would be
5.6417...
On the other hand, suppose the 5 numbers are
√5, 0, 0, 0, 0
the sum of their squares is indeed 5
and the sum of their cubes is (√5)^3 or 11
18...
how about that?
Was there more information?
Suppose you have 5 real numbers whose sum
of squares is equal to 5. What is the maximum
value of the sum of cubes of these 5 numbers?
Please show step
2 answers
and the sum of their cubes is (√5)^3 or 11.18...