If p and q are irrational numbers and $(p-3)\sqrt{5} + 4 = q\sqrt{5} + p$, how to find the values of p and q or (p+q).
2026-04-01 01:25:58.1775006758
Finding unknowns of an irrational equation .
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That's a single equation in two variables so there are an infinite number of (p, q) pairs that satisfy it. We can solve for one in terms of the other. For example, $(p- 3)\sqrt{5}+ 4- p= p(\sqrt{5}- 1)- 3\sqrt{5}+ 4= q\sqrt{5}$ so $q= \frac{\sqrt{5}-1}{\sqrt{5}}p- 3+ \frac{4\sqrt{5}}{5}$.
Take any (irrational) value for p and calculate the corresponding value of q.
For example, it we take $p= \sqrt{5}$, $q= \sqrt{5}- 1- 3+ \frac{4}{5}\sqrt{5}= \frac{9}{5}\sqrt{5}- 4$.