Question

For what value of ‘b’, the value of the expression $\left( {{a}^{3}}-b+2{{c}^{2}} \right)$ is 19, where a = 2 and c = 3?
A. 6
B. 7
C. 4
D. 5

Answer 1

Hint: We have an expression in a, b, c given to us. We have the value of expression as 19, so we can equate it. The values of a & c are also given. So, first we can substitute the value of a & c in the equation obtained. Then, after simplification, we can obtain the value of b.

Complete step-by-step answer:
The expression is given as $\left( {{a}^{3}}-b+2{{c}^{2}} \right)$which is equal to 19.
First, we have to understand what an expression is?
An expression in mathematics is a finite combination of symbols (such as valuable parameters, functions or brackets). For example:
$\begin{align}
  & 4x+5\left( \text{linear equation} \right) \\
 & a{{x}^{2}}+bx+c\left( \text{quadratic polynomial} \right) \\
\end{align}$
The expression which is given to us is $\left( {{a}^{3}}-b+2{{c}^{2}} \right)$. Now, we have also been given the value of this expression. The value of expression is given as 19, so we can equate them and then we will get an equation as shown below,
\[={{a}^{3}}-b+2{{c}^{2}}=19..............\left( 1 \right)\]
Now, we are given the value of a & c as a = 2 and c = 3.
Put these values of a & c in equation (1), from that we will find the value of b.
$\begin{align}
  & \Rightarrow {{2}^{3}}-b+2\times {{3}^{2}}=19 \\
 & \Rightarrow 8-b+2\times 9=19 \\
 & \Rightarrow 26-b=19 \\
 & \Rightarrow b=26-19 \\
 & \Rightarrow b=7 \\
\end{align}$
We have obtained the value of b = 7.
Hence the correct option is (B).

Note: We can also approach this question using the options given in the question. We can first substitute the values of a and c in the given expression, so we will get it as
$\begin{align}
  & 8-b+18 \\
 & \Rightarrow 26-b \\
\end{align}$
Now, we can substitute each option in the above and check which option gives the value of the above expression as 19. This method might be time consuming, so the method used in the solution must be preferred.