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Sa se afle valoarea expresie x² \ [(x²)²+x²+1] , stiind ca x\ (x²+x+1)=a

Răspuns :

Matepentrutoti
 x\ (x²+x+1)=a=>(x²+x+1)/x=1/a=>x+1+1/x=1/a=>x+1/x=1/a-1
(x+1/x)²=(1/a-1)²=
x²+2+1/x²=1/a²-2/a+1
x²+1/x²=1/a²-2/a-1
x² \ [(x²)²+x²+1] =(simplificam prin x²)=1/(x²+1+1/x²)=
=1/(1/a²-2/a-1+1)=1/(1/a²-2/a)=1/(1/a²-2a/a²)=a²/(1-2a)