Answer:
[tex]x=2\sqrt{2}[/tex], [tex]x=-2\sqrt{2}[/tex], [tex]x=4i[/tex], [tex]x=-4i[/tex]
Step-by-step explanation:
[tex]x^4+11x^2=3x^2+128[/tex]
First, we subtract 128 from both sides:
[tex]x^4+11x^2-128=3x^2[/tex]
Then, we subtract [tex]3x^2[/tex] from both sides:
[tex]x^4+8x^2-128=0[/tex]
Rewrite the equation:
[tex]u^2+8u-128=0[/tex]
Insert and solve:
[tex]u^2+8u-128=0\\u=8,u=-16\\x^2=8:x=2\sqrt{2},x= -2\sqrt{2} \\x^2=-16:x=4i,x=-4i[/tex]
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