Question

square of a number is eual to cube of some other number....find the final value which is equal on both sides .

Answer 1

${x}^{2} = {y}^{3} \\ this \: is \: only \: possible \: for \: 1 \: and \: 0$

Answer 2

$atq \: \\ {x}^{2} = {y}^{3 } \\ y = {x}^{6} \\ putting \: value \\ {x}^{2} = {y}^{3} \\ {x}^{2} = { {x}^{6} }^{3} \\ {x}^{2} = {x}^{18} \\ x = {x}^{9} \\ 1 = {x}^{8} \\ so \: x = \frac{ + }{ - } 1 \\ again \: putting \: values \: x = 1\: \\ {x}^{2} = {y}^{3 } \\ {1}^{2} = {y}^{3} \\ which \: gives \: y = 1 \: \:$
Therefore x=+- 1 and y=1 is right answer.