Let a,b,c,k be rational numbers such that k is not perfect cube if ` a + b k^(3/2) + c k^(2/3) = 0` prove that ` a = b = c =0`

Explanation

It is given that, `A C=\sqrt{3} B C`.


In a right-angle triangle `A B C`, it is right angled at `C`. Then, tangent `\backslash[{B} \backslash]` can be written as, `\tan B=\frac{\text { side opposite to angle } B}{\text { side adjacent to angle } B} \cdot` So,`\angle A B C=60^{\circ}`.


Hence proved.


Area `A=\frac{1}{2}(A B)(B C)`


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