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Joint Entrance Examination
Mathematics
Complex Numbers
Question 320
Question 320 of 455
Medium
MCQ
The sum of the roots of
x
2
+
∣
2
x
−
3
∣
−
4
=
0
x^2+|2x-3|-4=0
x
2
+
∣2
x
−
3∣
−
4
=
0
, is:
A
2
B
-2
C
2
\sqrt{2}
2
D
−
2
-\sqrt{2}
−
2
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Official solution
Case
x
≥
3
2
x\ge\dfrac32
x
≥
2
3
:
x
2
+
2
x
−
7
=
0
⟹
x
=
−
1
+
2
2
x^2+2x-7=0 \implies x=-1+2\sqrt{2}
x
2
+
2
x
−
7
=
0
⟹
x
=
−
1
+
2
2
(valid,
≥
3
2
\ge\dfrac32
≥
2
3
). Case
x
<
3
2
x<\dfrac32
x
<
2
3
:
x
2
−
2
x
−
1
=
0
⟹
x
=
1
−
2
x^2-2x-1=0 \implies x=1-\sqrt{2}
x
2
−
2
x
−
1
=
0
⟹
x
=
1
−
2
(valid,
<
3
2
<\dfrac32
<
2
3
). Sum
=
(
−
1
+
2
2
)
+
(
1
−
2
)
=
2
.
=(-1+2\sqrt{2})+(1-\sqrt{2})=\sqrt{2}.
=
(
−
1
+
2
2
)
+
(
1
−
2
)
=
2
.
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