ĐK \(a+b\ne0\)
Ta có \(\Delta=\left[\left(a-b\right)\left(a^2-b^2\right)\right]^2-4.\left(a+b\right)^2.\left(-2ab\right)\left(a^2+b^2\right)\)
\(=\left[\left(a-b\right)^2\left(a+b\right)\right]^2+8ab\left(a+b\right)^2\left(a^2+b^2\right)\)
\(=\left(a+b\right)^2\left[\left(\left(a-b\right)^2\right)^2+8ab\left(a^2+b^2\right)\right]\)
\(=\left(a+b\right)^2\left[\left(a^2-2ab+b^2\right)^2+8ab\left(a^2+b^2\right)\right]\)
\(=\left(a+b\right)^2\left[a^4+4a^2b^2+b^4-4a^3b-4ab^3+2a^2b^2+8a^3b+8ab^3\right]\)
\(=\left(a+b\right)^2\left[a^4+4a^2b^2+b^4+4a^3b+4ab^3+2a^2b^2\right]\)
\(=\left(a+b\right)^2.\left[\left(a^2+2ab+b^2\right)^2\right]=\left(a+b\right)^2\left(a+b\right)^4=\left(a+b\right)^6\)
Ta thấy \(\Delta=\left(a+b\right)^6>0\)với mọi \(a+b\ne0\)
Vậy phương trình luôn có 2 nghiệm phân biệt
