a sqrt a +b sqrt b = 183 and
a sqrt b + b sqrt a = 182
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Use the cubic expansion
and plug things in.
So
, which means that . Solve this for y to get .
Plug 9 - x in for y in
to get
.
Solve for x.
Go back to , and plug in your x-value to get y. Finally, plug into
and
to find a and b.
No more hints from me! You should be able to figure the rest out.
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