Determine Whether the Given Values Are Solutions of the Equation
Question:
Determine whether the given values are solution of the given equation or not:
\[ 2x^2-x+9=x^2+4x+3 \]
(i) \(x=2\)
(ii) \(x=3\)
Solution
A value of \(x\) is a solution if the left-hand side (LHS) becomes equal to the right-hand side (RHS).
Checking \(x=2\)
LHS:
\[ 2(2)^2-2+9 \]
\[ =8-2+9 \]
\[ =15 \]
RHS:
\[ (2)^2+4(2)+3 \]
\[ =4+8+3 \]
\[ =15 \]
Since LHS = RHS, \(x=2\) is a solution.
Checking \(x=3\)
LHS:
\[ 2(3)^2-3+9 \]
\[ =18-3+9 \]
\[ =24 \]
RHS:
\[ (3)^2+4(3)+3 \]
\[ =9+12+3 \]
\[ =24 \]
Since LHS = RHS, \(x=3\) is also a solution.
Answer
Both given values satisfy the equation.
\[ \boxed{x=2 \text{ and } x=3 \text{ are solutions}} \]