Question

Determinati numerele intregi x in fiecare dintre cazurile :
a)x²-x=4
b)x³-x²=100
AJUTOOOR >>>VA ROOOOG>> dau coronita

Answer 1

x²-x-4=0
x1,2=(1+-√(1+16))/2= (1+-√17)/2∉Z⇒adica, in Z, S=∅
de fapt x1,2∉R\Q


x²(x-1)=100=1*100=2*50=4*25=5*20=10*10=20*5=25*4=50*2=100*1

singura care convine este 25*4
x=5∈Z
x²=25
x-1=4

verificare 5³-5²=125-25=100 adevarat, bine rezolvat


poateca prima este tot asa ca a doua , adica
x³-x²=x²(x-1)=4=4*1=2*2=1*4
caz in care convine doar  x=2∈Z
x²=4
x-1=1

verificare 2³-2²=8-4=4 adevarat, binerezolvat