Question

Să se determine soluțiile întregi ale inecuației (x-1)² + x-7<0.

Answer 1

(x-1)² + x-7 < 0
(x-1)² = x²-2*x*1+1²
        = x² - 2x+1
x²-2x+1+x-7 < 0
x²-x+1 < 0
x²-x < 0-1
x²-x < -1
x < -1

Coroniţă+mulţumesc+5 steluţe ? :)

Answer 2

$(x-1)^2+x-7\ \textless \ 0 \\ x^2-2\cdot x \cdot 1+1^2+x-7\ \textless \ 0 \\ x^2-2x+1+x-7 \ \textless \ 0 \\ x^2-x-6\ \textless \ 0 \\ (x-3)(x+2)\ \textless \ 0 \\ x-3\ \textless \ 0 \\ x\ \textless \ 0+3 \\ x\ \textless \ 3 \\ x+2\ \textless \ 0 \\ x\ \textless \ 0-2 \\ x\ \textless \ -2$