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Question
secondary 3 | A Maths
4 Answers Below
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Date Posted: 4 years ago
Views: 238
If anyone can help solve this question it’d be greatly appreciated!
Alternative answer :
x¹⁄⁴ + x-¹⁄⁴ = 3
(x¹⁄⁴ + x-¹⁄⁴)⁴ = 3⁴
(x¹⁄⁴)⁴ + 4(x¹⁄⁴)³(x-¹⁄⁴) + 6(x¹⁄⁴)²(x-¹⁄⁴)² + 4(x¹⁄⁴)(x-¹⁄⁴)³ + (x-¹⁄⁴)⁴ = 81
(Binomial theorem expansion)
x + 4x¹⁄² + 6 + 4x¹⁄² + x-¹ = 81
x + 1/x = 81 - 6 - 4x¹⁄² - 4x-¹⁄²
x + 1/x = 81 - 6 + 8 - 4(x¹⁄² + 2 + x-¹⁄²)
x + 1/x = 83 - 4(x¹⁄⁴ + x-¹⁄⁴)²
x + 1/x = 83 - 4(3²) (from first equation)
= 83 - 36
= 47
x¹⁄⁴ + x-¹⁄⁴ = 3
(x¹⁄⁴ + x-¹⁄⁴)⁴ = 3⁴
(x¹⁄⁴)⁴ + 4(x¹⁄⁴)³(x-¹⁄⁴) + 6(x¹⁄⁴)²(x-¹⁄⁴)² + 4(x¹⁄⁴)(x-¹⁄⁴)³ + (x-¹⁄⁴)⁴ = 81
(Binomial theorem expansion)
x + 4x¹⁄² + 6 + 4x¹⁄² + x-¹ = 81
x + 1/x = 81 - 6 - 4x¹⁄² - 4x-¹⁄²
x + 1/x = 81 - 6 + 8 - 4(x¹⁄² + 2 + x-¹⁄²)
x + 1/x = 83 - 4(x¹⁄⁴ + x-¹⁄⁴)²
x + 1/x = 83 - 4(3²) (from first equation)
= 83 - 36
= 47
See 4 Answers
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This was the way I derived. Anyone who has an easier way feel free to answer because I think there should be an easier way nonetheless this works as well lol
Date Posted:
4 years ago
Probably a dual squaring or both sides
Thanks !!
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Alternatively, we can let y = x^1/4.
Date Posted:
4 years ago
Thank you! Really appreciate it
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An alternative idea
Date Posted:
4 years ago
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Pink part is the explanation, may help u uds Better
Date Posted:
4 years ago
Thank you for helping me out :-)
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