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\includegraphics[max width=\textwidth, alt={}, center]{e48188bc-3332-4248-971d-ebbbbbfb1280-14_807_1278_274_427}
The diagram shows curves with equations \(y = 2 x ^ { \frac { 1 } { 2 } } + 13 x ^ { - \frac { 1 } { 2 } }\) and \(y = 3 x ^ { - \frac { 1 } { 2 } } + 12\). The curves intersect at points \(A\) and \(B\).
- Find the coordinates of \(A\) and \(B\).
- Hence find the area of the shaded region.