Find the number of triples of real numbers (a, b, c) such that a²⁰+b²⁰+c²⁰=a²⁴+b²⁴+c²⁴=1 .

Step-by-step solution

a²⁰+b²⁰+c²⁰=a²⁴+b²⁴+c²⁴=1 If both equation have to satisfy Either a or b or c= 1 And other have to be 0 . So, if a=1 b=c=0 If a=-1 b=c=0 Similarly, for b and c if b= 1 a=c=0 And if c= 1 a=b=0 Total triples =6 .