Question

Calculati: (x-3)la patrat + 2(x+3)(x-2)+(x+2)+4x=
b)Aratati ca ( xla patrat-x+2)(x patrat -x-2)+4 este patratul unui numar real oricare ar fi x...
c) Calculati: x patrat+1/xpatrat stiind ca x-1/x=4 .
Va rog ajutati-ma la aceste exercitii...

Answer 1

(x-3)²+2(x+3)(x-2)+x+2+4x=
x²+9-6x+2(x²-2x+3x-6)+5x+2=
x²-x+11+2x²+2x-12=
=3x²+x-1

(x²-x+2)(x²-x-2)+4=
Notam a=x²-x
(a+2)(a-2)+4=
a²-4+4=
=a²=patrat perfect

x²+1/x²=?
x-1/x=4
(x-1/x)²=x²+1/x²-2·x·1/x
4²=x²+1/x²-2
x²+1/x²-2=16
x²+1/x²=18