In the following, determine whether the given values are solution… - Vidyadip

Question

In the following, determine whether the given values are solution of the given equation or not:
$2x^2 - x + 9 = x^2 + 4x + 3, x = 2, x = 3$

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Answer

$2x^2 - x + 9 = x^2 + 4x + 3, x = 2, x = 3$ When, $x = 2$
Substituting $x = 2$
$L.H.S. = 2x^2 - x + 9 = 2(2)^2 - 2 + 9$
$= 8 - 2 + 9 = 15$
$R.H.S. = x^2 + 4x + 3 = (2)^2 + 4 \times 2 + 3$
$= 4 + 8 + 3 = 15$
$\because$ L.H.S. = R.H.S.
$\therefore$ x = 2 is the solution
When, $x = 3$
$L.H.S. = 2x^2 - x + 9$
$= 2(3)^2 - 3 + 9$
$= 18 - 3 + 9 = 24$
$R.H.S. = x^2 + 4x + 3$
$= (3)^2 + 4 \times 3 + 3$
$= 9 + 12 + 3$
$= 24$
$\because$ L.H.S. = R.H.S.
$\therefore$ x = 3 is ths solution.

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