1966 AHSME Problems/Problem 22

Problem

Consider the statements: (I) $\sqrt{a^2+b^2}=0$ , (II) $\sqrt{a^2+b^2}=ab$ , (III) $\sqrt{a^2+b^2}=a+b$ , (IV) $\sqrt{a^2+b^2}=a - b$ , where we allow $a$ and $b$ to be real or complex numbers. Those statements for which there exist solutions other than $a=0$ and $b=0$ , are:

$\text{(A) (I),(II),(III),(IV)}\quad \text{(B) (II),(III),(IV) only} \quad \text{(C) (I),(III),(IV) only}\quad \text{(D) (III),(IV) only} \quad \text{(E) (I) only}$

Solution

$\fbox{A}$

1966 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 21	Followed by Problem 23
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1966 AHSME Problems/Problem 22

Problem

Solution

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