Question

14) Află numărul real .x, care verifică relația: a) x² = 2; b) x² = 4; c) x² = 11; d) 3x² = 9; e) 5x²= 25; f) x²+3=11; g) x²-2= 10.​

Answer 1

$\displaystyle a)~x^2=2\Rightarrow x=\pm\sqrt{2}\\\\b)~x^2=4\Rightarrow x=\pm \sqrt{4} \Rightarrow x=\pm2\\\\c)~x^2=11\Rightarrow x=\pm\sqrt{11}\\\\d)~3x^2=9 \Rightarrow x^2=\frac{9}{3}\Rightarrow x^2=3\Rightarrow x=\pm\sqrt{3}\\\\ e)~5x^2=25\Rightarrow x^2=\frac{25}{5}\Rightarrow x^2=5\Rightarrow x=\pm \sqrt{5}\\\\f)~x^2+3=11\Rightarrow x^2=11-3\Rightarrow x^2=8\Rightarrow x=\pm\sqrt{8}\Rightarrow x=\pm2\sqrt{2}$

$\displaystyle g)~x^2-2=10\Rightarrow x^2=10+2\Rightarrow x^2=12 \Rightarrow x=\pm \sqrt{12}\Rightarrow x=\pm 2\sqrt{3}$