Question

calcule x sendo:
3x²+⁴/x²=243

Answer 1

$3^{x^2+\frac{4}{x^2}}=243\\\\3^{x^2+\frac{4}{x^2}}=3^5\\\\x^2+\frac{4}{x^2}=5\\\\\frac{x^2.x^2+4}{x^2}+\frac{5.x^2}{x^2}\\\\x^4+4=5x^2\\\\x^4-5x^2+4=0\\\\x^2=A\\\\A^2-5A + 4 = 0\\\\\Delta = (-5)^2-4.1.4=9\\\\A_1=\frac{5+\sqrt{9}}{2}=\frac{5+3}{2}=4\\A_2=\frac{5-\sqrt{9}}{2}=\frac{5-3}{2}=1\\\\\\A = x^2\\x=\pm\sqrt{A_1} = \pm\sqrt{4}=\pm 2\\x=\pm\sqrt{A_2} = \pm\sqrt{1}=\pm 1$

Conjunto solução: {-2 , -1 , 1 , 2}