สำหรับข้อ 2. ผมทำแบบนี้ครับ.
\(\bf if\quad a + b + c = 0 \Rightarrow a^4 + b^4 + c^4 = 2(ab + bc + ca)^2 \)
\(\because \quad x + (2 -x) + (-2) = 0 \Rightarrow x^4 + (2-x)^4 + (-2)^4 = 2(2x-x^2-4+2x-2x)^2 = 2(x^2 - 2x + 4)^2 \)
\(\therefore \quad 2(x^2 - 2x + 4)^2 - 16 = 34 \Rightarrow (x^2 - 2x + 4)^2 = 5^2 \)
\( \therefore \quad x^2 - 2x - 1 = 0 \quad \cup x^2 - 2x + 9 = 0\)
\(\Rightarrow x = \frac{2\pm\sqrt{4+4}}{2} \quad \cup \quad x = \frac{2 \pm \sqrt{4 - 36}}{2}\)
\(\Rightarrow \quad x = 1 \pm \sqrt{2} \quad \cup \quad x = 1 \pm 2\sqrt{2}i \)
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