GMAT Resources Quadratic Equation.

[arjunnattar]

Hi,

In the GMAT resources for Math and in the Quadratic equations section do we have the explanations for the answers for the exercises. We have the answers printed but do we have the steps involved. If this has already been discussed can some one post the link for me?

[arjunnattar]

Can some one let me know how to solve this Quadratic equation with steps. I got this from our Forum under GMAT Resources Quadratic equations.

4^x-6.2^y-16=0.

[kanha81]

Can some one let me know how to solve this Quadratic equation with steps. I got this from our Forum under GMAT Resources Quadratic equations.

4^x-6.2^y-16=0.

Does this interpret as-

a) (4^x - 6) * (2^y - 16) = 0?
b) 4^x - (6*2^y) - 16 = 0?

Please be careful the way you ask us to help you solve the problem!!!

[arjunnattar]

it is actually

4^x - (6*2^y) - 16 = 0?

as written by you. I took this problem from the resources section. Sorry if it has caused any confusion.

[gmat740]

When dealing with Quadratic equations we must keep in mind that the equation has to be in one variable either x or y.However it have a degree of 2

eg: x^2+4x + 1 is a quad equation with variable x
However, x^2 + y^2 + 3x +4y + 1 =0
is also a Quadratic equation but since there are two variables,so the value cannot be determined solely by just one equation.

I think your question must be:

4^x - (6*2^y) - 16 = 0?

y has to be x

4^x - (6*2^x) - 16 = 0

Now
put 2^x =a

4^x=( 2^x)^2 = a^2

So equation can be written as

a^2 - 6a -16 = 0

(a-8)(a+2) = 0

a=8 or a=-2

2^x = 8
or 2^x = 2^3

x=3

also a= 2^x =-2(not possible, cannot have negative value!)

so x=3



Hope it Helps,

Karan

[arjunnattar]

Thanks Karan. I think we should update the section for Quadratic equations since i took the question from there.

[Vemuri]

When dealing with Quadratic equations we must keep in mind that the equation has to be in one variable either x or y.However it have a degree of 2

eg: x^2+4x + 1 is a quad equation with variable x
However, x^2 + y^2 + 3x +4y + 1 =0
is also a Quadratic equation but since there are two variables,so the value cannot be determined solely by just one equation.

I think your question must be:

4^x - (6*2^y) - 16 = 0?

I think the question was asking us to find the values of x & y. Inorder to make the quadratic equation=0, what should be the values of x & y? Incidentally, x & y both resolve to 3 in this case. How?

4^x = 6*2^y+16
The only values that satisfy this condition are x=3 & y=3
64 = 6*8+16
64 = 64

Consider another example, 4^x-3*2^y-10=0. In this case x=2 & y=1.

So, its not necessary that in an expression like the one mentioned above, there should be only 1 variable.

Hope this helps.

[gmat740]

I think the question was asking us to find the values of x & y. Inorder to make the quadratic equation=0, what should be the values of x & y? Incidentally, x & y both resolve to 3 in this case. How?

4^x = 6*2^y+16
The only values that satisfy this condition are x=3 & y=3
64 = 6*8+16
64 = 64

Consider another example, 4^x-3*2^y-10=0. In this case x=2 & y=1.

So, its not necessary that in an expression like the one mentioned above, there should be only 1 variable.

Hello,

I think we should work with those methods which are applicable to every question.
Putting numbers can work for specific questions only

take any two degree equations with 2 unknowns
try solving it with only one equation.Can you solve??

eg: x^2+y^2 = 9
or x^2-y^2 +4x-6y =13

etc etc.......there can numerous equation like this.

We need to have another equation to solve,Simply plugging in values won' t suffice.

[Vemuri]

Hello,

I think we should work with those methods which are applicable to every question.
Putting numbers can work for specific questions only

take any two degree equations with 2 unknowns
try solving it with only one equation.Can you solve??

eg: x^2+y^2 = 9
or x^2-y^2 +4x-6y =13

etc etc.......there can numerous equation like this.

We need to have another equation to solve,Simply plugging in values won' t suffice.

I was only trying to make sense out of what the question is asking instead of simply changing it to our convenience.

The question is using different variables as exponent values (4^x - 6*2^y - 16 = 0). What you are talking about is quadratic equations with 2 different variables (x^2+y^2 = 9). I agree that when 2 variables are involved, we need 2 equations to determine the values of the variables.

Anyway, I don't think it is still a valid question because it does not state if x & y are both integers. If they are fractions or negative numbers, we will not be able to determine the values of x & y.

[gmat740]

Anyway, I don't think it is still a valid question because it does not state if x & y are both integers. If they are fractions or negative numbers, we will not be able to determine the values of x & y

That's what I said and in fact just to solved it I changed that to a solvable question

The question is not Valid

I agree with you