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Mathematics
Mathematics
Problem
The complete set of values of 'a' for which the inequality
(
a
−
1
)
x
2
−
(
a
+
1
)
x
+
(
a
−
1
)
≥
0
(a-1)x^2-(a+1)x+(a-1)\ge 0
(
a
−
1
)
x
2
−
(
a
+
1
)
x
+
(
a
−
1
)
≥
0
is true for all
x
≥
2
x\ge 2
x
≥
2
. (a)
(
3
7
,
1
]
\left(\frac{3}{7}, 1\right]
(
7
3
,
1
]
(b)
(
−
∞
,
1
)
(-\infty, 1)
(
−
∞
,
1
)
(c)
(
−
∞
,
7
3
]
\left(-\infty, \frac{7}{3}\right]
(
−
∞
,
3
7
]
(d)
[
7
3
,
∞
)
\left[\frac{7}{3}, \infty\right)
[
3
7
,
∞
)
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