[tex]a_1 = 2x-3\\a_2 = x+1\\a_3 = x+3[/tex]
Z def. ciągu geometrycznego:
[tex]a_1\cdot a_3 = a_2^{2}\\\\(2x-3)(x+3) =(x+1)^{2}\\\\2x^{2}+6x-3x-9 = x^{2}+2x+1\\\\2x^{2}+3x-9 = x^{2}+2x+1\\\\2x^{2}-x^{2}+3x-2x-9-1 = 0\\\\x^{2}+x-10 = 0\\\\a = 1, \ b = 1, \ c = -10\\\\\Delta = b^{2}-4ac = 1^{2}-4\cdot1\cdot(-10) = 1+40 = 41[/tex]
[tex]x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-1-\sqrt{41}}{2}\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-1+\sqrt{41}}{2}[/tex]