Question

Remove the second term from the equation:
$x^3-6x^2+10x-3=0$.

Answer 1

Given equation $x^3–6x^2+10x–3=0$

Put $x=y+h\Rightarrow (y+h{)}^3–6(y+h{)}^2+10(y+h)–3=0$

$y^3+3y^{2}h+3y{h}^2+h^3–6(y^2+2hy+h^2)+10(y+h)–3=0$

$y^3+3y^{2}h+3y{h}^2+h^3–6y^2–12hy–6h^2+10y+10h–3=0$

$y^3+3(h–2)y^2+(3h^2–12h+10)y+(h^3–6h^2+10h–3)=0....\left(1\right)$

To remove second term we have $h–2=0\Rightarrow h=2$

Substituting $h=2$ in (1), required equation is:$y^3+(12–24+10)y+(8–24+20–3)=0$

$y^3–2y+1=0$