Równania z jedną niewiadomą. Oblicz: a) (x-2)^2+3x=(x+2)[mat]^2+2x-3 b) 2x- 3x+1/3=2x+ 5-4x/2 c) (x-[mat]\sqrt{2})(x+2\sqrt{2})=x^2-7\sqrt{2}x d) \sqrt{2}x-7=2x+3\sqrt{2} e) pix + 2=3x-7pi

a) (x-2)^2+3x=(x+2)^2+2x-3 x^2-4x+4+3x=x^2+4x+4+2x-3 -x+4=6x+1 -x-6x=1-4 -7x=-3 x=\frac{3}{7} b) 2x - \frac{3x+1}{3}=2x+ \frac{5-4x}{2} 12x -2 (3x+1)=12x+ 3(5-4x) 12x -6x-2=12x+ 15-12x 6x-2=15 6x=15+2 6x=17 x=\frac{17}{6}=2\frac{5}{6} c) (x-\sqrt{2})(x+2 \sqrt{2})=x^2-7 \sqrt{2} x x^2-\sqrt{2}x+2 \sqrt{2}x-4=x^2-7 \sqrt{2} x \sqrt{2}x+7 \sqrt{2} x=4 8\sqrt{2}x=4 x=\frac{4}{8\sqrt{2}}=\frac{1}{2\sqrt{2}}=\frac{\sqrt{2}}{4} d) \sqrt{2} x-7=2x+3 \sqrt{2} \sqrt{2} x-2x=7+3 \sqrt{2} x(\sqrt{2} -2)=7+3 \sqrt{2} x=\frac{7+3 \sqrt{2}}{\sqrt{2} -2}=\frac{(7+3 \sqrt{2})(\sqrt{2} +2)}{(\sqrt{2} -2)(\sqrt{2} +2)}=\frac{7\sqrt{2}+3 \cdot 2 +14+6\sqrt{2}}{2 -4} =-\frac{13\sqrt{2}+20}{2} e) \pi x+2=3x-7 \pi \pi x-3x=-2-7 \pi x(\pi -3)=-2-7 \pi x=\frac{-2-7 \pi}{\pi -3}

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