[tex]a_1 = 4\\a_2 = x-5\\a_3 = 26[/tex]
Z def. ciągu geometrycznego:
[tex]a_2^{2} = a_1\cdot a_3\\\\(x-5)^{2} = 4\cdot36\\\\x^{2}-10x+25 = 144\\\\x^{2}-10x+15-144 = 0\\\\\underline{x^{2}-10x-119 = 0}\\\\a = 1, \ b = -10, \ c = -119\\\\\Delta = b^{2}-4ac =(-10)^{2}-4\cdot1\cdot(-119) = 100 + 476 = 576\\\\\sqrt{\Delta} = \sqrt{576} = 24\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} =\frac{-(-10)-24}{2\cdot1} = \frac{10-24}{2} = \frac{-14}{2}=-7\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-(-10)+24}{2} = \frac{34}{2} = 14\\\\x\in\{-7,14\}[/tex]
