=> \(x^4-2015+\sqrt{x^2+2015}=0\)
<=> \(x^4-\left(x^2+2015\right)+x^2+\sqrt{x^2+2015}=0\)
<=> \(\left(x^2+\sqrt{x^2+2015}\right).\left(x^2-\sqrt{x^2+2015}\right)+\left(x^2+\sqrt{x^2+2015}\right)=0\)
<=> \(\left(x^2+\sqrt{x^2+2015}\right).\left(x^2-\sqrt{x^2+2015}+1\right)=0\)
=> \(x^2-\sqrt{x^2+2015}+1=0\) (*) (Vì \(x^2+\sqrt{x^2+2015}>0\) với mọi x )
Đặt \(\sqrt{x^2+2015}=t\Rightarrow x^2+2015=t^2\Rightarrow x^2=t^2-2015\)
thay vào (*) ta được: t2 - 2015 - t + 1 = 0
=> t2 - t - 2014 = 0
\(\Delta\) = 1 + 4. 2014 = 8057
=> \(t_1=\frac{1+\sqrt{8057}}{2};t_2=\frac{1-\sqrt{8057}}{2}\)
nhận t1 => x2 = \(\left(\frac{1+\sqrt{8057}}{2}\right)^2-2015\) => x = .....
