alpha/beta ²+beta/alpha ²
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2
Step-by-step explanation:
If alpha, beta are real and alpha^2, - beta^2 are the roots of a^2 x^2 + x + 1 - a^2 = 0; (a > 1) , then beta^2 =
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alpha^2, - beta^2 are the roots of a^2x^2 + x + 1 - a^2 = 0 alpha^2 - beta^2 = - 1/a^2, And alpha^2 ( - beta^2) = 1 - a^2a^2 (alpha^2 + beta^2)^2 = (alpha^2 ... More
Answered by
1
Answer:
Answer
α
2
,−β
2
are the roots of a
2
x
2
+x+1−a
2
=0
⇒α
2
−β
2
=−
a
2
1
,
And
⇒α
2
(−β
2
)=
a
2
1−a
2
(α
2
+β
2
)
2
=(α
2
−β
2
)
2
+4α
2
β
2
=
a
4
1
+4(
a
2
a
2
−1
)=
a
4
1
+4−
a
2
4
=(2−
a
2
1
)
2
⇒α
2
+β
2
=2−
a
2
1
β
2
=
2
1
[(α
2
+β
2
)−(α
2
−β
2
)]
=
2
1
[2−
a
2
1
+
a
2
1
]=1
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