Question

Rezolvati in R:
a) (x-1)(x-2)+3>(x-2)(x-5)+5
b) (x+7)^2 -4>(x+6)^2 -3
c) (x+1)^2 -(x+4)^2 ≤ (6-x)^2 -(3-x)^2

Answer 1

$\\ c)( x^{2} +2*x*1+ 1^{2} )-( x^{2} +2*x*4+ 4^{2} ) \leq ( 6^{2} -2*6*x+ x^{2} ) \\ -( 3^{2} -2*3*x+ x^{2} ) \\ x^{2} +2x+1- x^{2} -8x-16 \leq 36-12x+ x^{2} -9+6x- x^{2} \\ -6x-15 \leq -6x+27 \\ -6x+6x \leq 27+15 \\ 0 \leq 42 \\ Nu .Exista.Solutie!$$a) x^{2} -2x-x+2+3\ \textgreater \ x^{2} -5x-2x+10+5 \\ x^{2} -3x+5\ \textgreater \ x^{2} -7x+15 \\ x^{2} - x^{2} -3x+7x\ \textgreater \ 15-5 \\ 4x\ \textgreater \ 10 \\ x\ \textgreater \ \frac{10}{4}(simplificam.cu.2) \\ x\ \textgreater \ \frac{5}{2} \\ \\ b) x^{2}+2*x*7+ 7^{2} -4\ \textgreater \ x^{2} +2*x*6+ 6^{2} -3 \\ x^{2} +14x+49-4\ \textgreater \ x^{2} +12x+36-3 \\ x^{2} +14x+45\ \textgreater \ x^{2} +12x+33 \\ x^{2} - x^{2} +14x-12x\ \textgreater \ 33-45 \\ 2x\ \textgreater \ -12 \\ x\ \textgreater \ - \frac{12}{2} \\ x\ \textgreater \ -6$