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If x and z are positive constants, for how many values of y is

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If x and z are positive constants, for how many values of y is [#permalink] New post  04 Jun 2023, 10:45
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If x and z are positive constants, for how many values of y is x(y)^2 = z(y)^4?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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Re: If x and z are positive constants, for how many values of y is [#permalink] New post  04 Jun 2023, 22:57
achloes wrote:
If x and z are positive constants, for how many values of y is x(y)^2 = z(y)^4?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5


Given

  • x and z are positive constants

\(xy^2 = zy^4\)

\(y^2(x - zy^2)=0\)

Case 1: y = 0

Case 2: \(x - zy^2 = 0\)

\(x = zy^2\)

\(y^2 = \frac{x}{z}\)

\(|y| = \sqrt{\frac{x}{z}}\)

y can either take a positive or negative value.

Hence, three values of y are possible.

Option C
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Re: If x and z are positive constants, for how many values of y is [#permalink] New post  18 Jun 2023, 05:08
Hi, Bunuel can you please help me to identify where I am making a mistake?

I took 2 cases;

Case 1: x=z

then Y can take 2 values = -1 and 1

Case 2: x not equal to z

Then Y=0 or if we assume x=8 and z=2 then y can take 2 values -2 and 2

so in total, Y can take 5 values, -2,-1,0,1,2.
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Re: If x and z are positive constants, for how many values of y is [#permalink]
18 Jun 2023, 05:08
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