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Find a negative value of x that satisfies the equation [(x + 1)2 - (2x + 1)]1/2 + 2|x| - 6 = 0
A) -5
B) -4
C) -3
D) -2
E) -1
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[(x + 1)2 - (2x + 1)]1/2 + 2|x| - 6 = 0
From expansion,
(x + 1)2 = (x + 1)(x+1)
= x2 + 2x + 1
Substitute this into the initial equation
[x2 + 2x + 1 -(2x + 1)]1/2 + 2|x| - 6 = 0
[x2 + 2x + 1 -2x - 1]1/2 + 2|x| - 6 = 0
[x2]1/2 + 2|x| - 6 = 0
And, x1/2 = √x, Similarly (x2)1/2 = √x2 = x
x + 2|x| = 6
3x = 6
x = 6/3
x = 2
But since we want a negative value
x = -2
Ans D
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