a) x^2=2x x^2-2x=0 x(x-2)=0 x=0 lub x=2 b) x^2=-9x x^2+9x=0 x(x+9)=0 x=0 lub x=-9 c) 2x^2=7x 2x^2-7x=0 x(2x-7)=0 x=0 lub 2x-7=0 2x=7 x=3,5 d) x^2+9=6x x^2-6x+9=0 (x-3)^2=0 x-3=0 x=3 e) 4x^2+9=12x 4x^2-12x+9=0 (2x-3)^2=0 2x-3=0 2x=3 x=1,5 f) 121-x^2=0 x^2=121 x=11 lub x=-11 g) 9x^2=49 x^2=49/9 x=7/3 lub x=-7/3 h) x^2=-x x^2+x=0 x(x+1)=0 x=0 lub x=-1
a) [latex]x^{2}=2x\x^{2}-2x=0\x(x-2)=0\x=0 lub x-2=0\x=0 x=2\\x in {0; 2}[/latex] b) [latex]x^{2}=-9x \x^{2}+9x=0\x(x+9)=0\x=0 lub x+9=0\x=0 x=-9\\xin{-9; 0}[/latex] c) [latex]2x^{2}=7x\2x^{2}-7x=0\x(2x-7)=0\x=0 lub 2x-7=0\x=0 2x=7\x=0 x=3frac{1}{2}\\xin{0; 3frac{1}{2}}[/latex] d) 1 sposób: [latex]x^{2}+9=6x \x^{2}-6x+9=0\Delta=b^{2}-4ac=(-6)^{2}-4*1*9=36-36=0\x=frac{-b}{2a}=frac{6}{2}=3\\xin{3}[/latex] 2 sposób: [latex]x^{2}+9=6x\x^{2}-6x+9=0\(x-3)^{2}=0 o wzor: (a-b)^{2}=a^{2}-2ab+b^{2}\x-3=0\x=3\\x in {3}[/latex] e) 1 sposób: [latex]4 x^{2} +9=12x\4 x^{2} -12+9=0\Delta=b^{2}-4ac=(-12)^{2}-4*4*9=144-144=0\x=frac{-b}{2a}=frac{12}{8}=frac{3}{2}=1frac{1}{2}\\x in{1frac{1}{2}}[/latex] 2 sposób: [latex]4 x^{2} +9=12x\4 x^{2} -12x+9=0\(2x-3)^{2}=0 o wzor: (a-b)^{2}=a^{2}-2ab+b^{2}\2x-3=0\2x-3=0\2x=3\x=frac{3}{2}\x=1frac{1}{2}\\xin {1frac{1}{2}}[/latex] f) [latex]121-x^{2}=0\-x^{2}=-121\x^{2}=121\x=11 lub x=-11\\x in {-11; 11}[/latex] g) [latex]9 x^{2} =49\x^{2}=frac{49}{9}\\x=frac{7}{3} lub x=-frac{7}{3}\\x=2frac{1}{3} lub x=-2frac{1}{3}\\xin {-2frac{1}{3}; 2frac{1}{3}} [/latex] h) [latex]x^{2}=-x\x^{2}+x=0\x(x+1)=0\x=0 lub x+1=0\x=0 x=-1\\x in {-1; 0}[/latex]
