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Question
In the following, determine whether the given values are solutions of the given equation or not:
2x2 - x + 9 = x2 + 4x + 3, x = 2, x =3
Solution
We have been given that,
2x2 - x + 9 = x2 + 4x + 3
2x2 - x + 9 - x2 - 4x - 3 = 0
x2 - 5x + 6 = 0, x = 2, x = 3
Now if x = 2 is a solution of the equation then it should satisfy the equation.
So, substituting x = 2 in the equation, we get
x2 - 5x + 6
= (2)2 - 5(2) + 6
= 4 - 10 + 6
= 0
Hence x = 2 is a solution of the given quadratic equation
Also, if x = 3 is a solution of the equation then it should satisfy the equation.
So, substituting x = 3 in the equation, we get
x2 - 5x + 6
= (3)2 - 5(3) + 6
= 9 - 15 + 6
= 0
Hence x = 3 is a solution of the quadratic equation.
Therefore, from the above results we find out that both x = 2 and x = 3 are solutions of the quadratic equation.
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