A) \[\text{x}=-\text{1},\text{y}=-\text{1}\]
B) \[~\text{x}=\text{1},\text{ y}=\text{1}\]
C) \[\text{x}=\text{1},\text{ y}=\text{2}\]
D) \[\text{x}=\text{2},\text{y}=\text{1}\]
Correct Answer: B
Solution :
Given \[\text{1}0\text{4}=\text{16}\times \text{6}+\text{8}\] \[16=8\times 2+0\] Equate any two equations: \[\text{256}=\text{8}\times \text{32}+0\] \[3465={{3}^{2}}\times 5\times 7\times 11\] \[\text{546}0=\text{22}\times \text{3}\times \text{5}\times \text{7}\times \text{l3}\] \[\therefore \] ??.(1) And \[={{2}^{2}}\times {{3}^{2}}\times 5\times 7\times 11\times 13=180180\] \[\therefore \] \[H.C.F.=\frac{\text{Product of the numbers}}{L.C.M.}\] .....(2) Solving eq (1) and (2), we get y = 1 and \[\text{5474}=\text{2}\times \text{7}\times \text{17}\times \text{23}\]. The solution of equations is \[\text{9775}={{\text{5}}^{\text{2}}}\times \text{17}\times \text{23}\].
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