SOLUTION: PLEASE HELP ME PLEASE IF ANYONE CAN IF(P-Q)^2=25 AND PQ=14,WHAT IS THE VALUE OF (P+Q)^2?

Question 924373: PLEASE HELP ME PLEASE IF ANYONE CAN
IF(P-Q)^2=25 AND PQ=14,WHAT IS THE VALUE OF (P+Q)^2?
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Let's use lower-case for the variables and try a solution.

, , and you want to find .

, first equation partially simplified;

Substitute using the second equation:

Another substitution again using from the second equation:

Solution first for p^2.----------------, this method will be long and very detailed...

-----------------------------------------------------------------------------
Maybe another way.

from the first equation.

.
-
Using this q in the next equation of pq=14,

p=-2 OR p=7
OR

p=2 OR p=-7

Again, looking at the pq=14 equation, p and q must be of the same sign so that their product is POSITIVE 14. This means that their solutions must be:
---------------------------
p=-2 and q=-7
OR
p=2 and q=7.
---------------------------

The exercise question asked for was, find .
Using either combination of p and q found, this expression will be .
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