Respuesta :
Answer:
The solutions are: [tex]x=4,\:x=-4,\:x=3i,\:x=-3i[/tex]
Step-by-step explanation:
Consider the provided equation.
[tex]x^4-7x^2-144=0[/tex]
Substitute [tex]u=x^2\mathrm{\:and\:}u^2=x^4[/tex]
[tex]u^2-7u-144=0[/tex]
[tex]u^2-16u+9u-144=0[/tex]
[tex](u-16)(u+9)=0[/tex]
[tex]u=16,\:u=-9[/tex]
Substitute back [tex]\:u=x^2[/tex] and solve for x.
[tex]x^2=16\\x=\sqrt{16}\\ \quad x=4,\:x=-4[/tex]
Or
[tex]x^2=-9\\x=\sqrt{-9}\\ \quad x=3i,\:x=-3i[/tex]
Hence, the solutions are: [tex]x=4,\:x=-4,\:x=3i,\:x=-3i[/tex]
Check:
Substitute x=4 in provided equation.
[tex]4^4-7(4)^2-144=0[/tex]
[tex]256-112-144=0[/tex]
[tex]0=0[/tex]
Which is true.
Substitute x=-4 in provided equation.
[tex](-4)^4-7(-4)^2-144=0[/tex]
[tex]256-112-144=0[/tex]
[tex]0=0[/tex]
Which is true.
Substitute x=3i in provided equation.
[tex](3i)^4-7(3i)^2-144=0[/tex]
[tex]81+63-144=0[/tex]
[tex]0=0[/tex]
Which is true.
Substitute x=-3i in provided equation.
[tex](-3i)^4-7(-3i)^2-144=0[/tex]
[tex]81+63-144=0[/tex]
[tex]0=0[/tex]
Which is true.
