731 prompts matching "Forming an equation whose roots are alpha over beta and beta over alpha"
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Worked Example: Adding two surds that simplify to the same root
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Common Mistakes: Rationalising when both terms of the denominator are surds
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Worked Example: Squaring both sides safely when solving a surd equation
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Spot My Mistake: Solving a surd equation that leads to a quadratic
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Common Mistakes: A surd equation that has no real solution
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Learn: What closure means for a binary operation
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Learn: What it means for an operation to be commutative
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Worked Example: Testing whether star distributes over plus
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Practice: Multiplication distributing over addition in ordinary arithmetic
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Learn: What an identity element is
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Learn: Reading index notation, the base and the exponent
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Learn: Why any non-zero number to the power nought is one
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Practice: A fractional index with numerator one, read as a root
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Common Mistakes: Writing a root as a fractional index before simplifying
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Show All Working: Solving a simple logarithmic equation
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Common Mistakes: Rejecting a root that makes a logarithm undefined
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Learn: The change of base formula
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Common Mistakes: A logarithmic equation that becomes a quadratic
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Learn: What a sequence is, and what a term means
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Learn: What makes a sequence an arithmetic progression
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