If x4 + 2x3 + ax2 + bx + 9 is a perfect square where a and b are positive real numbers, then the value of a and b is?

Answer: Option B

$$\begin{array}{rl}& x^4+2x^3+a{x}^2+bx+9\\ & \text{Put }x=1\\ & =1+2\times 1+a+b+9\\ & =1+2+a+b+9\\ & =13+a+b\end{array}$$
To make a perfect square numbers value of a + b must be either 3 or 13
Now, option (B) a = 6, b = 7
$$\begin{array}{rl}& \therefore a+b=13\\ & \text{make perfect square}\\ & \left(25=5^2\right)\end{array}$$