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Date Posted: 3 years ago
Views: 668
Let x = √(4 + √15) + √(4 - √15)
x² = [√(4 + √15) + √(4 - √15)]²
x² = (√(4 + √15))² + 2 √(4 + √15) √(4 - √15) + (√(4 - √15))²
x² = 4 + √15 + 2√[(4+√15)(4-√15)] + 4 - √15
x² = 8 + 2√(4² - (√15)²)
x² = 8 + 2√(16 - 15)
x² = 8 + 2√1
x² = 8 + 2
x² = 10
x = √10 or x = -√10 (rejected as x is the product of two positive square roots and so x cannot be negative)
x² = [√(4 + √15) + √(4 - √15)]²
x² = (√(4 + √15))² + 2 √(4 + √15) √(4 - √15) + (√(4 - √15))²
x² = 4 + √15 + 2√[(4+√15)(4-√15)] + 4 - √15
x² = 8 + 2√(4² - (√15)²)
x² = 8 + 2√(16 - 15)
x² = 8 + 2√1
x² = 8 + 2
x² = 10
x = √10 or x = -√10 (rejected as x is the product of two positive square roots and so x cannot be negative)
See 2 Answers
done
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clear
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Rough idea
Date Posted:
3 years ago
Missing the square root symbol for (√(4 - √15))²
Wow, this is what happens when there are too many square roots in an expression.
Maybe putting it in indices format would reduce the occurrence of careless mistakes .
Maybe putting it in indices format would reduce the occurrence of careless mistakes .
Two √ still okay.
Three, four, five, etc, will be hard to keep track.
Brackets too. That's why I prefer to use some [ ] sometimes instead of many ( )
Three, four, five, etc, will be hard to keep track.
Brackets too. That's why I prefer to use some [ ] sometimes instead of many ( )
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