If a - 1/a = 10 ; find: a + 1/a , a ^ 2 - 1/(a ^ 2)
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Step-by-step explanation:
a-\frac{1}{a}=\pm 4a−
a
1
=±4
Step-by-step explanation:
Given : a^2+\frac{1}{a^2}=18a
2
+
a
2
1
=18
To find : The value of a-\frac{1}{a}a−
a
1
?
Solution :
Using identity,
(x-y)^2=x^2+y^2-2xy(x−y)
2
=x
2
+y
2
−2xy
Let x=ax=a and y=\frac{1}{a}y=
a
1
Substitute in the identity,
(a-\frac{1}{a})^2=a^2+\frac{1}{a^2}-2\times a\times \frac{1}{a}(a−
a
1
)
2
=a
2
+
a
2
1
−2×a×
a
1
(a-\frac{1}{a})^2=18-2(a−
a
1
)
2
=18−2
(a-\frac{1}{a})^2=16(a−
a
1
)
2
=16
Taking root both side,
a-\frac{1}{a}=\pm 4a−
a
1
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