(a+1/a)²-(a-1/a)² pls answer me...
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1
Step-by-step explanation:
As, (a+b)²=a²+2ab+b²
(a–b)²=a²–2ab+b²
( a + \frac{1}{a} )^{2} - (a - \frac{1}{a} )^{2}(a+
a
1
)
2
−(a−
a
1
)
2
=
=( \frac{a ^{2} + 1}{a} ) {}^{2} - ( \frac{a {}^{2} - 1}{a} ) {}^{2}(
a
a
2
+1
)
2
−(
a
a
2
−1
)
2
=( \frac{(a {}^{2} + 1) {}^{2} }{a {}^{2} } ) - ( \frac{ ({a}^{2} + 1) {}^{2} }{a {}^{2} } )(
a
2
(a
2
+1)
2
)−(
a
2
(a
2
+1)
2
)
=\frac{a {}^{4} + 2a {}^{2} + 1}{a {}^{2} } - ( \frac{a {}^{4} - 2a {}^{2} + 1 }{a {}^{2} } )
a
2
a
4
+2a
2
+1
−(
a
2
a
4
−2a
2
+1
)
=\frac{ {a}^{4} + 2a {}^{2} + 1 - {a}^{4} +2a {}^{2} - 1 }{a {}^{2} }
a
2
a
4
+2a
2
+1−a
4
+2a
2
−1
=\frac{4a {}^{2} }{a {}^{2} }
a
2
4a
2
= 4=4
Answer is '4'!
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