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Question Number 191394 by Mingma last updated on 23/Apr/23

	Answered by Rasheed.Sindhi last updated on 23/Apr/23
	$(√a) +((2022)/( (√b) ))=2023 2023(√b) −(√a) (√b) =2022 (√b) (2023−(√a) )=2×3×337 { (((√b) =2 ∧ 2023−(√a) =3×337)),(((√b) =3 ∧ 2023−(√a) =2×337)),(((√b)=337 ∧ 2023−(√a) =2×3 )),(((√b) =2×3 ∧ 2023−(√a) =337)),(((√b) =2×337 ∧ 2023−(√a) =3)),(((√b) =3×337 ∧ 2023−(√a) =2)),(((√b) =2×3×337 ∧ 2023−(√a) =1)) :} { ((b =4 ∧ a =(2023−3×337)^2 )),((b =9 ∧ a =(2023−2×337)^2 )),((b=337^2 ∧ a =(2023−2×3)^2 )),((b =36 ∧ a =(2023−337)^2 )),((b =674^2 ∧ a =(2023−3)^2 )),((b =1011^2 ∧ a =(2023−2)^2 )),((b =2023^2 ∧ a =(2023−1)^2 )) :}$
	$\sqrt{a} + \frac{2022}{\sqrt{b}} = 2023$ $2023 \sqrt{b} - \sqrt{a} \sqrt{b} = 2022$ $\sqrt{b} (2023 - \sqrt{a}) = 2 \times 3 \times 337$ ${\begin{cases} \sqrt{b} = 2 \land 2023 - \sqrt{a} = 3 \times 337 \\ \sqrt{b} = 3 \land 2023 - \sqrt{a} = 2 \times 337 \\ \sqrt{b} = 337 \land 2023 - \sqrt{a} = 2 \times 3 \\ \sqrt{b} = 2 \times 3 \land 2023 - \sqrt{a} = 337 \\ \sqrt{b} = 2 \times 337 \land 2023 - \sqrt{a} = 3 \\ \sqrt{b} = 3 \times 337 \land 2023 - \sqrt{a} = 2 \\ \sqrt{b} = 2 \times 3 \times 337 \land 2023 - \sqrt{a} = 1 \end{cases}$ ${\begin{cases} b = 4 \land a = {(2023 - 3 \times 337)}^{2} \\ b = 9 \land a = {(2023 - 2 \times 337)}^{2} \\ b = 337^{2} \land a = {(2023 - 2 \times 3)}^{2} \\ b = 36 \land a = {(2023 - 337)}^{2} \\ b = 674^{2} \land a = {(2023 - 3)}^{2} \\ b = 1011^{2} \land a = {(2023 - 2)}^{2} \\ b = 2023^{2} \land a = {(2023 - 1)}^{2} \end{cases}$
	Commented by Mingma last updated on 23/Apr/23
	Very nice solution, sir!
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