[tex]\it a)\ \ x^2+3^2=5^2 \Rightarrow x^2=5^2-3^2=(5-3)(5+3)=2\cdot6=16 \Rightarrow \\ \\ \Rightarrow \sqrt{x^2}=\sqrt{16} \Rightarrow |x|=4 \Rightarrow x=\pm4 \Rightarrow x_1=-4;\ \ x_2=4[/tex]
[tex]\it b)\ \ 13-x^2=5^2 \Rightarrow 13^2-5^2=x^2 \Rightarrow x^2=(13-5)(13+5)=8\cdot18 \Rightarrow \\ \\ \Rightarrow x^2=414 \Rightarrow \sqrt{x^2}=\sqrt{144} \Rightarrow |x|=12 \Rightarrow x=\pm12 \Rightarrow x_1=-12,\ x_2=12[/tex]
[tex]\it d)\ 2x^2-162=288\Big|_{:2} \Rightarrow x^2-81=144\Big|_{+81} \Rightarrow x^2=225 \Rightarrow \\ \\ \Rightarrow \sqrt{x^2}=\sqrt{225} \Rightarrow |x|=15 \Rightarrow x=\pm15 \Rightarrow x_1=-15,\ \ x_2=15[/tex]
[tex]\it e)\ \ 25^2-5x^2=20^2 \Rightarrow 25^2-20^2=5x^2 \Rightarrow (25-20)(25+20)=5x^2 \Rightarrow \\ \\ \Rightarrow 5\cdot45=5x^2\Big|_{:5} \Rightarrow 45=x^2 \Rightarrow x^2=45 \Rightarrow \sqrt{x^2}=\sqrt{45} \Rightarrow |x|=\sqrt{9\cdot5} \Rightarrow \\ \\ \Rightarrow x=\pm3\sqrt5 \Rightarrow x_1=-3\sqrt5,\ \ x_2=3\sqrt5[/tex]
