It is given that $a$ and $b$ are positive integers such that \(\left( a\sqrt{5}-1 \right)\left(

Question

It is given that $a$ and $b$ are positive integers such that $\left( a\sqrt{5}-1 \right)\left( \sqrt{5}+b \right)=20\sqrt{5}+32$. Form a pair of simultaneous equations and solve them to find the value of $a$ and of $b$.

Accepted Answer

$a=7,\ b=3$

Surds - Equating Rational and Irrational Parts

Surds - Equating Rational and Irrational Parts

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