SOLUTION: p^2+q^2=85, p-q=1,then p^2-q^2=?

Question 759039: p^2+q^2=85, p-q=1,then p^2-q^2=?
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
p^2+q^2=85, p-q=1,then p^2-q^2=?
-------
p = 1+q
-----
Equation:
(1+q)^2 + q^2 = 85
1 + 2q + 2q^2 = 85
----------------------------------
2q^2 + 2q - 84 = 0
------
q^2 + q - 42 = 0
----
Factor:
(q+7)(q-6) = 0
---------------------
q = 6 or q = -7
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Solve for "p"
p - q = 1
If q = 6, p = 7
If q = -7, p = -6
-----
p^2-q^2=?

P^2 - q^2 = 6^2-7^2 = -13
OR
p^2 - q^2 = 7^2 - 6^2 = 13
========================
Cheers,
Stan H.
====================
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

,
if ,then ........plug it in

...divide all by

......use quadratic formula

solutions:

or

now find

or

so, there are two solutions:
1. and
2. and

then

or

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