Discussion
If p and q are positive, p2 + q2 = 16, and p2 – q2 = 8, then q =
*This question is included in Introduction to Nova GRE Math, question #10
| (A) | 2 |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 06/24/2012 21:46
Can you explain how you are subtracting the equations from one another? I am just not seeing it from the example given.
Posted: 06/25/2012 02:33
Step by step:
Posted: 06/25/2012 09:45
thank you so much
Posted: 07/24/2012 15:18
Why do you subtract the equations?
Posted: 07/24/2012 16:50
Katie, recall from Algebra. If you have two equations with two unknowns, you can eliminate one unknown at a time in order to solve for the remaining unknown.
Posted: 11/05/2012 21:17
Can you explain why you are dividing the equation by 2? Why 2? Why divide at all?
Posted: 11/05/2012 22:22
Mike, we divide the equation by 2 because we want to solve for q, so divide by 2 to get rid of q's unit variable.
Posted: 11/24/2012 09:41
When you subtract the equation how do you get 2q squared. One q is positive and the other is negative... Shouldn't they cancel each other out?
Posted: 11/24/2012 17:51
Janice,
Common properties:
4 + 4 = 8
4 - 4 = 0
4 + (+4) = 8
4 - (-4) = 8
4 + (-4) = 0
4 - (+4) = 0
Thus addition will cancel out q
p^2 + q^2 = 16
p^2 - q^2 = 8
--------------------- addition
p^2 + (+p^2) = 2p^2
q^2 + (-q^2) = 0
16 + (+8) = 24
Niels
Common properties:
4 + 4 = 8
4 - 4 = 0
4 + (+4) = 8
4 - (-4) = 8
4 + (-4) = 0
4 - (+4) = 0
Thus addition will cancel out q
p^2 + q^2 = 16
p^2 - q^2 = 8
--------------------- addition
p^2 + (+p^2) = 2p^2
q^2 + (-q^2) = 0
16 + (+8) = 24
Niels
Posted: 12/03/2012 13:37
Can we apply substitution as well?
Posted: 12/03/2012 15:20
Ngoc,
p^2 + q^2 = 16
p^2 = 16 - q^2
(16 - q^2) - q^2 = 8
16 - q^2 - q^2 = 8
-2q^2 = 8 - 16
-2q^2 = -8
q^2 = 4
q = sqrt(4)
q = 2
Niels
p^2 + q^2 = 16
p^2 = 16 - q^2
(16 - q^2) - q^2 = 8
16 - q^2 - q^2 = 8
-2q^2 = 8 - 16
-2q^2 = -8
q^2 = 4
q = sqrt(4)
q = 2
Niels
Posted: 03/19/2013 19:31
What mistake am I making wrong here:
I set the equations equal to q^2.
Q^2=16-p^2
Q^2=p^2-8
16-p^2=p^2-8
24=2p^2
12=p^2
Why doesn't this work?
I set the equations equal to q^2.
Q^2=16-p^2
Q^2=p^2-8
16-p^2=p^2-8
24=2p^2
12=p^2
Why doesn't this work?
Posted: 03/19/2013 19:35
Gia, you didn't do anything wrong. The question is asking for q, not p^2. So you just need to continue a few more steps.
Posted: 07/03/2013 07:59
Is the substitution method inapplicable here cuz I tried it and I got q=1....I need help
Posted: 07/03/2013 08:02
It's clear to me now
Posted: 09/25/2013 07:54
Is this how the question is going to be stated in the test? How do I know to subtract the second equation from the first?
Posted: 10/07/2013 16:44
Cara, this is one type of question that will be asked in the test. This is basic algebra, solving for a system of equation with unknowns. When you have two equations with two unknowns (a and b, for example), you can solve the equations for a and b. There are 2 ways to solve: 1) by subtracting one from another to eliminate a or b; 2) by substitution.
Posted: 10/20/2014 05:17
Does this solution violate order of operations by dividing both sides by 2 before taking the square route of both sides? I don't see any parenthesis or am I missing something?
Posted: 10/20/2014 12:30
Brandon, in the second step from last, the explanation divides both sides of the equation by 2, in order to get q^2=4. Then you factor q^2-4=0, to get (q-2)(q+2)=0, and q=-2 and 2.
I do not like the wording of the explanation (taking the square root of both sides), because mathematically speaking it is not accurate. The square root of 4 is 2, not -2 and 2. But when we factor out q^2-4=0, we do get q=-2 and q=2.
I hope that helps.
I do not like the wording of the explanation (taking the square root of both sides), because mathematically speaking it is not accurate. The square root of 4 is 2, not -2 and 2. But when we factor out q^2-4=0, we do get q=-2 and q=2.
I hope that helps.
Posted: 10/21/2014 01:01
Hi Brandon,
The order of operations acronym PEMDAS is the general rule for performing operations in an expression.
When solving equations, the rule is performed in reverse order: SADMEP.
So, we divide before taking the square root. However, taking the square root first would give the same answer. The guidelines SADMEP and PEMDAS can often be violated.
Nova Press
The order of operations acronym PEMDAS is the general rule for performing operations in an expression.
When solving equations, the rule is performed in reverse order: SADMEP.
So, we divide before taking the square root. However, taking the square root first would give the same answer. The guidelines SADMEP and PEMDAS can often be violated.
Nova Press