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21 Apr 2022, 07:45
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For some values of x, the expression \(\frac{x^{(a^3)}}{x^{(ab^2)}}\) is negative. If a and b are integers, which of the following must be true?
A. a is positive
B. a is even
C. b is positive
D. b is even
E. b is odd
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
A. a is positive
B. a is even
C. b is positive
D. b is even
E. b is odd
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
27 Apr 2022, 18:53
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\begin{aligned}\dfrac{x^{a^{3}}}{x^{ab^{2}}}=x^{a^{3}-ab^{2}}\\
=x^{a\left( a^{2}-b^{2}\right) }\\
=x^{a\left( a+b\right) \left( a-b\right) }\end{aligned}
That's as far as I've gotten. Not sure if this is even the correct way to do this.
=x^{a\left( a^{2}-b^{2}\right) }\\
=x^{a\left( a+b\right) \left( a-b\right) }\end{aligned}
That's as far as I've gotten. Not sure if this is even the correct way to do this.
27 Apr 2022, 23:13
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Bunuel
For some values of x, the expression \(\frac{x^{(a^3)}}{x^{(ab^2)}}\) is negative. If a and b are integers, which of the following must be true?
A. a is positive
B. a is even
C. b is positive
D. b is even
E. b is odd
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
A. a is positive
B. a is even
C. b is positive
D. b is even
E. b is odd
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
Imo C
\(\frac{x^{(a^3)}}{x^{(ab^2)}}\) is negative implies that x is negative
x<0
Now for the expression to be negative that power have to odd
So a*(a+b)*(a-b) = Odd
If a is even then whole expression becomes even, so a is odd
If both are odd then again the whole expression becomes even so both can not be odd
So b is even now have odd*(odd+even)*(odd-even) = odd
So the expression is negative
So b is even
So D is our answer
