Question

The value of 'a' for which the system of equations $(a+1{)}^{3}x+(a+2{)}^{3}y=(a+3{)}^3$, $(a+1)x+(a+2)y=a+3$ ,$x+y=1$ is consistent ,is

• A. -2
• B. -1
• C. 1
• D. 2

Answer 1

The correct option is A -2

For consistent systems
$\left|\begin{array}{ccc}(a+1{)}^3& (a+2{)}^3& (a+3{)}^3\\ a+1& a+2& a+3\\ 1& 1& 1\end{array}\right|=0$
$\Rightarrow (a+1{)}^3(-1)-(a+2{)}^3(-2)+(a+3{)}^3(-1)=0$
$\Rightarrow (a+2{)}^3-(a+1{)}^3+(a+2{)}^3-(a+3{)}^3=0$
$\Rightarrow \left(1\right)(3a^2+9a+7)+(-1)(3a^2+15a+19)=0$
$\Rightarrow -6a-12=0$
$\therefore a=-2$