Question

2a - 3 radical din 5 = b radical din -7
a,b=?

Answer 1

$2a-3 \sqrt{5}=b \sqrt{5}-7 \Rightarrow a= \frac{b \sqrt{5}-7+3 \sqrt{5} }{2} \in Q. \\ \\ \frac{b \sqrt{5} -7+3 \sqrt{5} }{2} \in Q \Rightarrow b \sqrt{5}+3 \sqrt{5} =\sqrt{5}(b+3) \in Q \Rightarrow b=-3. \\ \\ a= \frac{-3 \sqrt{5}-7+3 \sqrt{5} }{2} = -\frac{7}{2} . \\ \\ \underline{Solutie}:~(a,b)= \Big( -\frac{7}{2}; -3 \Big) .$