2017-II-12 – Solving Master

Ans: C
Let

y = k_{1} + k_{2} x^{2}

, where

k_{1}

and

k_{2}

are non-zero constants.

When $x = 1$ , $y = 7$ . We have

$\begin{array}{rcl} 7 & = & k_{1} + k_{2} (1)^{2} \\ k_{1} + k_{2} & = & 7 \dots ① \end{array}$

When $x = 2$ , $y = 13$ . We have

$\begin{array}{rcl} 13 & = & k_{1} + k_{2} (2)^{2} \\ k_{1} + 4 k_{2} & = & 13 \dots ② \end{array}$

$② - ①$ , we have

$\begin{array}{rcl} 3 k_{2} & = & 6 \\ k_{2} & = & 2 \end{array}$

Sub. $k_{2} = 2$ into $①$ , we have

$\begin{array}{rcl} k_{1} + 2 & = & 7 \\ k_{1} & = & 5 \end{array}$

Therefore, $y = 5 + 2 x^{2}$ . If $x = 3$ , then we have

$\begin{array}{rcl} y & = & 5 + 2 (3)^{2} \\ y & = & 23 \end{array}$