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Fractional indices, conjugates and exact surd relationships
Free examples and worked answers. No account needed.
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Fractional indices, conjugates and exact surd relationships
Optional enrichment: Fractional indices, conjugates and exact surd relationships
Example 1
u=√21+2√5. Find u2+u21.
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Answer: 82
- Since 21−20=1,u1=√21−2√5.
- Thus u+u1=2√21, and u2+u21=4×21−2.
Example 2
For x>0,x21×x31=4630. Find x.
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Answer: 4096
- Combine the left indices to get x65.
- Raise both sides to 56:x=46=4096.
Example 3
u=√19+3√2. Find u2+u21.
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Answer: 74
- Since 19−18=1,u1=√19−3√2.
- Thus u+u1=2√19, and u2+u21=4×19−2.
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