If z 2-1 - z 2-11 then find the value of z 3-1 - z 3

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Byju's Answer

Standard IX

Mathematics

Identity (x-y)^2

If z 2+1 / z ...

Question

If z²+(1/z²)=11 then find the value of z³-(1/z³)

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Solution

(z²+1/z²)=11
(z-1/z)²=z²+1/z²-2
(z-1/z)²=11-2
(z-1/z)²=9
z-1/z=√9=3

(z-1/z)³=3^3

z³-1/z³-3(z-1/z)=27
z³-1/z³-3×3=27
z³-1/z³=27+9
z³-1/z³=36

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If z²+(1/z²)=11 then find the value of z³-(1/z³)

(z²+1/z²)=11 (z-1/z)²=z²+1/z²-2 (z-1/z)²=11-2 (z-1/z)²=9 z-1/z=√9=3 (z-1/z)³=3^3 z³-1/z³-3(z-1/z)=27 z³-1/z³-3×3=27 z³-1/z³=27+9 z³-1/z³=36

(z²+1/z²)=11
(z-1/z)²=z²+1/z²-2
(z-1/z)²=11-2
(z-1/z)²=9
z-1/z=√9=3

(z-1/z)³=3^3

z³-1/z³-3(z-1/z)=27
z³-1/z³-3×3=27
z³-1/z³=27+9
z³-1/z³=36