Question

x la puterea 4 plus 2x la puterea 2 minus 3 egal 0

Answer 1

[tex]x^4+2x^2-3=0 \Leftrightarrow x^4-x^2+3x^2-3=0 \Leftrightarrow \\\;\\ \Leftrightarrow x^2(x^2-1)+3(x^2-1) = 0 \Leftrightarrow (x^2-1)(x^2+3)=0\ \ \ (1) \\\;\\ x^2+3 \ \textgreater \ 0, pentru\ oricare\ x \in\mathbb{R}\ \ \ (2) \\\;\\ Din \ relatiile\ (1), (2) \Rightarrow x^2-1=0 \Rightarrow x^2=1 \Rightarrow \sqrt{x^2} =\sqrt1\Rightarrow \\\;\\ \Rightarrow |x|=1 \Rightarrow x=\pm1 \\\;\\ Deci,\ ecuatia\ data\ are\ doua\ solutii\ reale\ :\ x_1=-1,\ \ \ x_2=1 . [/tex]