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Question
Solve the following equation:
3√12−x+3√14+x=2
3√12−x+3√14+x=2
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Solution
Cubing on both sides12−x+14+x+3(12−x)2/3(14+x)1/3+3(14+x)2/3(12−x)1/3=8(12−x)2/3(14+x)1/3+(14+x)2/3(12−x)1/3=−6
Cubing on both sides(12−x)2(14+x)+(14+x)2(12−x)+6(12−x)2(14+x)2=−216⟹x=−15,13
12−x+14+x+3(12−x)2/3(14+x)1/3+3(14+x)2/3(12−x)1/3=8
(12−x)2/3(14+x)1/3+(14+x)2/3(12−x)1/3=−6
Cubing on both sides
(12−x)2(14+x)+(14+x)2(12−x)+6(12−x)2(14+x)2=−216
⟹x=−15,13
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