Solve for t(advanced rational equations)

t² -7 + 12t⁻² = 0Multiply each side by t² :t⁴ -7t² + 12 = 0This is a quadratic equation in the variable ' t² '.For just a moment, to avoid confusion, let U = t².Then the equation isU² - 7U + 12 = 0whence(U - 4) (U - 3) = 0andU = 4   and   U = 3 .Now we can go back to ' t² ' in place of U :t² = 4t = +2  and  t = -2t² = 3t = +√3  and  t = -√3                                       

[tex]t^2-7+12t^{-2}=0\\
t^4-7t^2+12=0\\
t^4-3t^2-4t^2+12=0\\
t^2(t^2-3)-4(t^2-3)=0\\
(t^2-4)(t^2-3)=0\\
(t-2)(t+2)(t^2-3)=0\\
t=2 \vee t=-2 \vee t=-\sqrt{3}\vee t=\sqrt3
[/tex]