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Oj dużo tego, ale jedziemy z tym koksem. a)[latex] 2x^{2} + 3sqrt{3}x - 9 = 0\ Delta = b^{2} - 4ac\ Delta = (3sqrt{3})^{2} - 4*2*(-9)\ Delta = 27+72\ Delta = 99\ x_{1} = frac{-b - sqrt{Delta}}{2a}\ x_{1} = frac{-3sqrt{3} - sqrt{99}}{4}\ x_{2} = frac{-b + sqrt{Delta}}{2a}\ x_{2} = frac{-3sqrt{3} + sqrt{99}}{4}\[/latex] b)[latex]5x^{2}+sqrt{5}x+frac{1}{5} = 0\ Delta = 5 -4\ Delta = 1\ x_{1} = frac{-sqrt{5} - 1}{10}\ x_{2} = frac{-sqrt{5} + 1}{10}[/latex] c)[latex]x^{2} +3=sqrt{3}x\ x^{2} - sqrt{3}x+3= 0\ Delta = 3 - 12\ Delta = -9\[/latex] Nie ma miejsc zerowych. d) [latex]2sqrt{2}(1+x^{2}-sqrt{2}) = 4(sqrt{2}x - 1)\ 2sqrt{2} + 2sqrt{2}x^{2} - 4 = 4sqrt{2}x - 4\ 2sqrt{2} + 2sqrt{2}x^{2} - 4 - 4sqrt{2}x + 4 = 0\ 2sqrt{2}x^{2} - 4sqrt{2}x+2sqrt{2} = 0\ Delta = 32 - 4*2sqrt{2}*2sqrt{2}\ Delta = 32-32\ Delta= 0\ x = frac{4sqrt{2}}{4sqrt{2}}\ x=1 [/latex] e) [latex](sqrt{7}x+1)(sqrt{7}-x)=3(2sqrt{7}-x)\ 7x-sqrt{7}x^{2}+sqrt{7}+x = 6sqrt{7}-3x\ 7x-sqrt{7}x^{2}+sqrt{7}+x - 6sqrt{7}+3x=0\ sqrt{7}x^{2}+11x-5sqrt{7} = 0\ Delta = 261\ x_{1} = frac{-11 - sqrt{261}}{2sqrt{7}} x_{2} = frac{-11+ sqrt{261}}{2sqrt{7}}[/latex] f)[latex](2sqrt{2}x+1)^{2}-2x(sqrt{2}+x) = 2frac{1}{6}\ 8x + 4sqrt{2}x+1 - 2sqrt{2}x+2x^{2} - 2frac{1}{6} = 0\ 2x^{2} + (8+2sqrt{2})x-frac{7}{6} = 0\ Delta = (8+2sqrt{2})^{2} - 4*2*(-frac{7}{6})\ Delta = 64+32sqrt{2}+4+frac{56}{6}\ Delta = 74+32sqrt{2}\ x_{1} = frac{-8-2sqrt{2}-sqrt{74+32sqrt{2}}}{4}\ x_{2} = frac{-8-2sqrt{2}+sqrt{74+32sqrt{2}}}{4}[/latex]