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Question Number 190907 by mustafazaheen last updated on 14/Apr/23

$$\mathrm{how}\mathrm{is}\mathrm{explanotory}\mathrm{solution}$$$$4^{{\mathrm{x}}^2+3\mathrm{x}+2}+4^{{\mathrm{x}}^2+3\mathrm{x}+7}=4^{{2\mathrm{x}}^2+6\mathrm{x}+9}+1$$$$\mathrm{x}=?$$

Answered by Frix last updated on 14/Apr/23

$$4^{(x+1)(x+2)}+4^{(x+1)(x+2)+5}=4^{2(x+1)(x+2)+5}+1$$$$t=4^{(x+1)(x+2)}$$$$t+4^{5}t=4^5{t}^2+1$$$$t^2-\frac{1025t}{1024}+\frac{1}{1024}=0$$$$(t=\frac{1}{1024})\vee t=1$$$$x\in \mathbb{R}:x=-2\vee x=-1$$$$(x\notin \mathbb{R}:x=-\frac{3}{2}\pm \frac{\sqrt{19}}{2}\mathrm{i})$$

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