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2026 NYGH P2 Q2

2026 NYGH P2 Q2

IP 4
7 marks
  1. Express \(\dfrac{1+\sqrt2}{5-\sqrt2}\) in the form \(p+q\sqrt2\), where \(p\) and \(q\) are rational numbers.[3]
  2. Find the value of \(x\) for which \(\log_3(x^2+3x)-2\log_3 x=2\log_9 5\).[4]

Solution:

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Answer:(a) \(\dfrac7{23}+\dfrac6{23}\sqrt2\) (b) \(x=\dfrac34\)

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