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# If r = and s = p тАУ q, for which of the

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Intern
Joined: 07 May 2003
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If r = and s = p тАУ q, for which of the [#permalink]

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13 May 2003, 17:14
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If r = and s = p тАУ q, for which of the following values of p would r^2 = s^2 ?
(A) 1/5q
(B) 10-3/5q
(C) q-1
(D) 3q
(E) 9/2q-9
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14 May 2003, 12:24
r^2 = s^2

=> 1/4(3p+q)^2 = (p-q)^2

solve for P : p= 1/5q or -3q

A = 1/5q

Last edited by tzolkin on 15 May 2003, 06:03, edited 2 times in total.
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14 May 2003, 17:12
I think none.......

r^2 = s^2 implies that it wants us to prove whether r = s or r = -s

substitute for r = s

(3p+q)/2 = p-q

3p+q = 2p-2q

p=-3q

substitute r = -s

(3p+q)/2 = -(p-q)

3p+q = -2p +2q

5p = q

p = q/5

so none of the answer choices match.......choices seem to be wrong
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14 May 2003, 17:14
I think that ans A is in fact : 1/5 * q NOT 1/(5q)

This is how I interpreted it ?
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15 May 2003, 06:06
=> 1/4(3p+q)^2 = (p-q)^2

9P^2+6pq+q^2=4p^2-8pq-4q^2

5p^2+14pq-3q^2=0

(5p-q)(p+3q)=0

p = 1/5 * q and -3q
15 May 2003, 06:06
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