Hii
if x = 2 + √3
find x² + 1/x² and x³ + 1/x³
plzz, it is branliest question...
Answers
Answered by
147
Hi there !
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Given :
x = 2 + √3
To Find :
(i) x² + 1 / x²
(ii) x³ + 1 / x³
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x = 2 + √3
1 / x = 1 / 2 + √3
1 / x = 1 / 2 + √3 × 2 - √3 / 2 - √3
1 / x = 2 - √3 / (2)² - (√3)²
1 / x = 2 - √3 / 4 - 3
1 / x = 2 - √3
Now,
x + 1 / x = 2 + √3 + 2 - √3
x + 1 / x = 2 + 2
x + 1 / x = 4
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Question I :
x + 1/x = 4
On squaring both sides ..
( x + 1/x )² = (4)²
x² + 1 / x² + 2 = 16
x² + 1 / x² = 16 - 2
x² + 1 / x² = 14 [Ans]
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Question II :
x + 1 / x = 4
On cubing both sides ..
( x + 1/x )³ = (4)³
x³ + 1/x³ + 3 ( x + 1/x) = 64
x³ + 1/x³ + 3 (4) = 64
x³ + 1/x³ + 12 = 64
x³ + 1/x³ = 64 - 12
x³ + 1/x³ = 52 [Ans]
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Thanks for the question !
☺️☺️
undertalker:
great you is best
Answered by
93
Here is your solution
x = 2 + √3
x = 2 + √3
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