Question

Se stie ca x+1supra x=4.Calculati:xla puerea4+1supra x la puterea 4 .Ce metoda sau rationament se foloseste ?

Answer 1

se folosesc  ridicarile la patrat

x+1/x=4

atunci (x+1/x)²=4²

x²+2*1/x * x+(1/x)²=16

x²+2+1/x²=16

x²+1/x²=16-2=14

(x²+1/x²)²=14²=196

(x²)²+2*x²*1/x²+(1/x²)²=196

x^4+2+1/x^4=196

x^4+1/x^4=194