If |-2 + 3 + 8 - 12 | = m2 + n3 , then what is the value

Question

If  |-\sqrt{2}+\sqrt{3}+\sqrt{8}-\sqrt{12}| = m\sqrt{2} + n\sqrt{3} , then what is the value of  m - n ?

A. -2
B. -1
C. 0
D. 1
E. 2

Bunuel · Answer

|-\sqrt{2}+\sqrt{3}+\sqrt{8}-\sqrt{12}| = m\sqrt{2} + n\sqrt{3}

|-\sqrt{2}+\sqrt{3}+2\sqrt{2}-2\sqrt{3}| = m\sqrt{2} + n\sqrt{3}

|\sqrt{2}-\sqrt{3}| = m\sqrt{2} + n\sqrt{3} 
 
Since  \sqrt{2}-\sqrt{3} < 0 , then  |\sqrt{2}-\sqrt{3}| =-(\sqrt{2}-\sqrt{3})

-\sqrt{2}+\sqrt{3} = m\sqrt{2} + n\sqrt{3}

Now, either the question should mention that m and n are integers, then only  m=-1  and  n=1  work. Hence, m - n = -2

Or, the question is flawed becasue m - n can be any value if m and n are not necessarily integers. For example, m - n = 0 for  m = \frac{\sqrt{3} -\sqrt{2}}{\sqrt{2} + \sqrt{3}}  and  n = \frac{\sqrt{3} -\sqrt{2}}{\sqrt{2} + \sqrt{3}}

Not a good question.

If |-2 + 3 + 8 - 12 | = m2 + n3 , then what is the value

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­If |-2 + 3 + 8 - 12 | = m2 + n3 , then what is the value

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If |-2 + 3 + 8 - 12 | = m2 + n3 , then what is the value