Cambridge Question (1 Viewer)

[xXnukerrrXx]

From 8C question 9. The interval PQ has length p and the point A lies between P and Q. Find PA if PA^2=PQ X QA. Thanks =D

 

[Hermes1]

posting the solution in a second...

 

[Hermes1]

well u no that:
PQ = p
and A lies between P and Q
and PQ X QA = PA^2

therefore since PQ = p and QA = PQ - PA = p - AP
p(p-AP) = PA^2
therefore p^2 - pPA = PA^2
PA^2 + pPA - p^2 = 0
then using quadratic formula solve for PA. u shuld take the positive value only (since it is a distance) and u shuld get (-1 + root5)p/2

edit : forgot the p in the answer

 

[SpiralFlex]

Let

We are given

So now,







Solve and disregard the negative solution,

 

[Drongoski]

From 8C question 9. The interval PQ has length p and the point A lies between P and Q. Find PA if PA^2=PQ X QA. Thanks =D

Let PA = x; .: QA = p-x

.: since PQ x QA = PA^2: p(p-x) = x²



Solving quadratic equation we get 2 values of x: ignoring the negative one.

 

[xXnukerrrXx]

thanks guys =D