Expand and simplify $(7 + \sqrt{5})(3 - \sqrt{5})$ - Edexcel - A-Level Maths Pure - Question 4 - 2010 - Paper 2
Question 4
Expand and simplify $(7 + \sqrt{5})(3 - \sqrt{5})$.
Express \( \frac{7 + \sqrt{5}}{3 + \sqrt{5}} \) in the form \( a + b\sqrt{5} \), where \( a \) and \( b \) are i... show full transcript
Worked Solution & Example Answer:Expand and simplify $(7 + \sqrt{5})(3 - \sqrt{5})$ - Edexcel - A-Level Maths Pure - Question 4 - 2010 - Paper 2
Step 1
Expand and simplify $(7 + \sqrt{5})(3 - \sqrt{5})$
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Answer
To expand the expression, we use the distributive property:
Multiply each term in the first bracket by each term in the second bracket:
(7)(3)+(7)(−5)+(5)(3)+(5)(−5)
This results in:
21−75+35−5
Now combine like terms:
21−5+(−75+35)
Simplifying gives:
16−45
Step 2
Express \( \frac{7 + \sqrt{5}}{3 + \sqrt{5}} \) in the form \( a + b\sqrt{5} \)
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Answer
To express ( \frac{7 + \sqrt{5}}{3 + \sqrt{5}} ) in the form ( a + b\sqrt{5} ):
First, multiply the numerator and the denominator by the conjugate of the denominator, which is ( 3 - \sqrt{5} ):
