Question

Rezolvati inecuatiile in multimea numerelor intregi: a) (x-1) la puterea a 2+x mai mic decat(x-1)(x+1)-x
b) (x -4) la puterea a doua+3(x la a doua + 5x) mai mic sau egal(2x+3) la puterea a doua -5(x-4)+7

Answer 1

a) x²-2x+1+x< x²-1-x
1<-1 (F) => x € multimii vide
b) x²-8x+16+3x²+15x<=4x²+12x+9-5x+20+7
16<=36 (A) => x € |R

Answer 2

a)

(x-1)²+x<(x-1)(x+1)-x

x²-2x+1+x<x²-1-x

x²-x+1<x²-1-x

-x+1<-1-x

1-x<-1-x

1<-1

Nu are soluții.

b)

(x-4)²+3(x²+5x)≤(2x+3)²-5(x-4)+7

x²-8x+16+3x²+15x≤4x²+12x+9-5x+20+7

4x²+7x+16≤4x²+7x+36

7x+16≤7x+36

16≤36

Număr infinit de soluții.