x = -1/4 is an extraneous solution.
✓(11x + 3) - 2x = 0
Adding 2x on both sides of the equation we get
✓(11x + 3) - 2x + 2x = 0 + 2x
✓(11x + 3) = 2x
Squaring both sides of the equation we get
(✓(11x + 3))² = (2x)²
11x + 3 = 4x²
4x² - 11x - 3 = 0 : Equation 1
By middle term splitting equation 1 can be written as
4x² - 12x + x - 3 = 0
4x(x - 3) + 1(x - 3) = 0
(4x + 1)(x - 3) = 0
x = - 1/4 and 3.
Check extraneous solution by putting the value of x in the original equation -
Let x = -1/4
✓(11(-1/4) + 3) - 2(-1/4) = 0
✓(-11/4 + 3) + (1/2) = 0
✓(1/4) + (1/2) = 0
1/2 + 1/2 = 0
1 = 0
which is a contradiction, so, x = -1/4 is an extraneous solution.
Let x = 3
✓(11×3 + 3) - 2×3 = 0
✓36 - 6 = 0
6 - 6 = 0
0 = 0
Since, LHS = RHS, x = 3 is not an extraneous solution.
Know more about extraneous solutions -
brainly.com/question/1511979
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