\(\left(2x^2+3\right)^2-10x^2-15x=0\)
\(\Leftrightarrow4x^4+12x^2+9-10x^2-15x=0\)
\(\Leftrightarrow4x^4+2x^2-15x+9=0\)
\(\Leftrightarrow4x^4-4x^2+6x^2-6x-9x+9=0\)
\(\Leftrightarrow4x^2\left(x^2-1\right)+6x\left(x-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow4x^2\left(x-1\right)\left(x+1\right)+6x\left(x-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[4x\left(x+1\right)+6x-9\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(4x^2+10x-9\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(4x^2+10x+\frac{25}{4}+\frac{11}{4}\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[\left(2x+\frac{5}{2}\right)^2+\frac{11}{4}\right]=0\)
Vì \(\left(2x+\frac{5}{2}\right)^2+\frac{11}{4}>0\)
=> x - 1 = 0
=> x = 1
Vậy x = 1
