Official Solution
Steps 1 & 2: Understand Question and Draw Inferences
Given : Integersa,b,x
- •\(a^6=b^3=\frac{|x|}{x}\)
\(\frac{|x|}{x}\) can take two possible values:
- •If \(x > o, |x| = x, \frac{|x|}{x}=\frac{x}{x}=1\)
•If \(x < o, |x| = -x, \frac{|x|}{x}=−\frac{x}{x}=−1\)
- •\(a^6=\frac{|x|}{x}\)
•As\(a^6\) is alwayspositive,\(a^6 = 1\) , i.e.\(a = 1\) or\(-1\)
•So, we can reject the value of\(\frac{|x|}{x}=−1\)
•\(b^3=\frac{|x|}{x}=1\)
•b = 1
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