if (z²+1/z²) =18, find the value of z³-1/z³, using only the positive value of z-1/z..
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Answered by
44
(z²+1/z²)=18
(z-1/z)²=z²+1/z²-2
(z-1/z)²=18-2
(z-1/z)²=16
z-1/z=√16=4
(z-1/z)³=4³
z³-1/z³-3(z-1/z)=64
z³-1/z³-3×4=64
z³-1/z³=64+12
z³-1/z³=76
(z-1/z)²=z²+1/z²-2
(z-1/z)²=18-2
(z-1/z)²=16
z-1/z=√16=4
(z-1/z)³=4³
z³-1/z³-3(z-1/z)=64
z³-1/z³-3×4=64
z³-1/z³=64+12
z³-1/z³=76
Anonymous:
thank u so much..
Answered by
16
Given ,
z² +1/z² = 18
subtracting 2 ( z/z) from both sides
=> z² + 1/z² - 2 z * 1/z = 18 - 2
= > ( z-1/z )² = 16
Therefore , z - 1/z = 4
we know that ,
a³ - b³ = (a - b ) ( a² + b² + ab )
=> z³ - 1/z³ = ( 4 ) ( 18 + z/z)
z³ - 1/z³ = 76
z² +1/z² = 18
subtracting 2 ( z/z) from both sides
=> z² + 1/z² - 2 z * 1/z = 18 - 2
= > ( z-1/z )² = 16
Therefore , z - 1/z = 4
we know that ,
a³ - b³ = (a - b ) ( a² + b² + ab )
=> z³ - 1/z³ = ( 4 ) ( 18 + z/z)
z³ - 1/z³ = 76
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