[tex]a_1 = -3\\a_2 = x+4\\a_3 = -48[/tex]
Z własności ciągu geometrycznego:
[tex]a_2^{2} = a_1\cdot a_2\\\\(x+4)^{2}= -3\cdot(-48)\\\\x^{2}+8x+16 = 144\\\\x^{2}+8x+16-144\\\\x^{2}+8x-128\\\\a = 1, \ b = 8, \ c = -128\\\\\Delta = b^{2}-4ac = 8^{2}-4\cdot1\cdot(-128) = 64 + 512 = 576\\\\\sqrt{\Delta} = \sqrt{576} = 24\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-8-24}{2\cdot1} = \frac{-32}{2} = -16\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-8+24}{2} = \frac{16}{8} = 8\\\\x \in\{-16, 8\}[/tex]
