Solve the quadratic equation using formula:
a (x2 + 1) = (a2 + 1) x, a is not equal to 0
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Answer:
Step-by-step explanation:
Correct option is
A
{
a
1
,a}
Given equation is a(x
2
+1)=x(a
2
+1)
⇒ ax
2
+a=a
2
x+x
⇒ ax
2
−a
2
x−x+a=0
⇒ ax
2
−(a
2
+1)x+a=0
⇒ a=a,b=−(a
2
+1),c=a
⇒ x=
2a
−b±
b
2
−4ac
=
2(a)
−[−(a
2
+1)]±
[−(a
2
+1)]
2
−4(a)(a)
=
2a
a
2
+1±
a
4
+2a
2
+1−4a
2
=
2a
a
2
+1±
a
4
−2a
2
+1
=
2a
a
2
+1±
(a
2
−1)
2
=
2a
a
2
+1±(a
2
−1)
⇒ x=
2a
a
2
+1+a
2
−1
and x=
2a
a
2
+1−a
2
+1
⇒ x=
2a
2a
2
and x=
2a
2
∴ x=a and x=
a
1
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