Question

tìm các số nguyên a;b;c sao cho \(a^2\le b;b^2\le c;c^2\le a\)

Answer 1

Ta có:a²<_b=>(a²)⁴<_b⁴=>a⁸<_b⁴

          b²<_c=>(b²)²<_c²=>b⁴<_c²

          c²<_a

=>a⁸<_b⁴<_c²<_a

=>a⁸<_a

=>a⁸=a=>a⁸=b⁴=c²=a

=>a⁸-a=0

=>a.(a⁷-1)=0

=>a=0=>b⁴=c²=1=>b=c=1=>a=b=c=1

hoặc a⁷-1=0=>a⁷=1=>a=1=>b⁴=c²=0=>b=c=0=>a=b=c=0

Vậy a=b=c=0,a=b=c=1