Question

Factorise and solve:
x² (a-b)x=(c-a)(c-b)​

Answer 1

Answer:

The solution is

$x=-(a-c),\,-(c-b)$​

Step-by-step explanation:

$\text{Given:}$

$x^2+(a-b)x=(c-a)(c-b)$​

$\implies\,x^2+(a-b)x-(c-a)(c-b)=0$​

$\implies\,x^2+(a-b)x+(a-c)(c-b)=0$​

$\implies\,x^2+(a-c+c-b)x+(a-c)(c-b)=0$​

$\implies\,x^2+(a-c)x+(c-b)x+(a-c)(c-b)=0$​

$\implies\,x(x+(a-c))+(c-b)(x+(a-c))=0$​

$\implies\,\boxed{\bf\,(x+(a-c))(x+(c-b))=0}$​

$\implies\,x+(a-c)=0\:(or)\:x+(c-b)=0$​

$\implies\,\boxed{\bf\,x=-(a-c)\:(or)\:x=-(c-b)}$​