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Joint Entrance Examination
Mathematics
Complex Numbers
Question 319
Question 319 of 455
Medium
MCQ
The equation
3
x
2
+
x
+
5
=
x
−
3
\sqrt{3x^2+x+5}=x-3
3
x
2
+
x
+
5
=
x
−
3
, where
x
x
x
is real, has:
A
no solution
B
exactly one solution
C
exactly two solutions
D
exactly four solutions
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Solutions · 1
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Official solution
Squaring:
3
x
2
+
x
+
5
=
x
2
−
6
x
+
9
⟹
2
x
2
+
7
x
−
4
=
0
⟹
x
=
1
2
3x^2+x+5=x^2-6x+9 \implies 2x^2+7x-4=0 \implies x=\dfrac12
3
x
2
+
x
+
5
=
x
2
−
6
x
+
9
⟹
2
x
2
+
7
x
−
4
=
0
⟹
x
=
2
1
or
−
4
-4
−
4
. Neither satisfies the original equation (RHS must be
≥
0
\ge0
≥
0
, but at these values the equation fails to hold), so there is no solution.
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