Question

Rezolvati inecuatiile:
Bipatrate!
[tex] a^{4}- a^{2} -2=0
[/tex]
[tex]- t^{4} -7t^{2} +8=0
[/tex]
Incomplete
$3x^{2}-4x=0$
$2x^2-6x=0$
$x^2-25=0$
$2x^2-200=0$
Va rog rpd dau 50 de puncte

Answer 1

[tex]a^4-a^2-2=0\\ Not. a^2=k\\ k^2-k-2=0\\ \Delta=1+8=9\Rightarrow \sqrt{\Delta}=3\\ k_1=\frac{1+3}{2}=2\\ k_2=\frac{1-3}{2}=-1\\ Daca: a^2=2\Rightarrow a=\pm\sqrt{2}\\ Daca: a^2=-1(imposibil)\\ S:a\in \{\pm \sqrt2\}\\ \\ -t^4-7t^2+8=0\\ Not. t^2=k\\ -k^2-7k+8=0\\ \Delta=49+32=81\Rightarrow \sqrt{\Delta}=9\\ k_1=\frac{7+9}{-2}=-8\\ k_2=\frac{7-9}{-2}=1\\ Daca:t^2=-8(imposibil)\\ Daca: t^2=1\Rightarrow t\in \{\pm1\}\\ S:t\in \{\pm 1\}\\[tex]3x^2-4x=0\\ x(3x-4)=0\\ i)x_1=0\\ ii)3x-4=0\Rightarrow x_2=\frac{4}{3}\\ S:x\in \{0,\frac{4}{3}\}\\ \\ 2x^2-6x=0\\ 2x(x-3)=0\\ i)2x=0\Rightarrow x_1=0\\ ii)x-3=0\Rightarrow x_2=3\\ S: x\in \{0;3\}[/tex]
[tex]x^2-25=0\\ x^2=25\\ |x|=5\\ S:x\in \{\pm 5\}\\ \\ 2x^2-200=0\\ 2x^2=200|:2\\ x^2=100\\\ |x|=10\\ S:x\in \{\pm 10\}[/tex]