Square root math prolblem... and more,,,?

Question

Square Root of(36x^2+24xy+4y^2=Square Root of(9x^2+54xy+81y^2
then which of the following expressions could be equal to y?

If x=x^2+y^2/-2y and y is not equal to 0 then y is equal to which of the following?

If x is not equal to -3/2, 2x^3-x^2-6x/2x+3

If x and y are both positive numbers and x^2+2xy+y^2=121

kind of get nervous with problems with x^2 and all and i dont know how to solve these please explain

the first one multiple choice

A)y=-2x B) y=e-9/1x C)y=-3/7x D)y==9/11x E)y=3x

If x=x^2+y^2/-2y and y is not equal to 0 then y is equal to which of the following?

A) -2x-x^2 B ) x^2-y/2 C) x^2+y/-2 D)-x E) x

If x is not equal to -3/2, 2x^3-x^2-6x/2x+3

A) x-2 B) 2x-2 C) x^2-2x D) 2x^2-2 E) 2x^2-2x

If x and y are both positive numbers and x^2+2xy+y^2=121

x^2 is x to the 2nd power which is x times x

Answer 1

This lesson appears to be all about recognizing perfect squares of expressions.

(x + y)^2 = x^2 + 2xy + y^2
(ax + by)^2 = a^2x^2 + 2abxy + b^2y^2

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(1) Both of the expressions in the square roots are perfect squares, when factored:

sqrt( (6x + 2y)^2 ) = sqrt( (3x + 9y)^2 )

This means, either:

6x + 2y = 3x + 9y

or else:

6x + 2y = -(3x + 9y)

Solving those equations for y:

6x + 2y = 3x + 9y
7y = 3x
y = (7/3)x

6x + 2y = -(3x + 9y)
11y = -9x
y = -(9/11)x

Those are the two solutions for y which are possible given the information that you entered. y = either (7/3)x or -(9/11)x. One of those appears to match your multiple choice.

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(2) x = x^2 + y^2 / -2y

I'm assuming both x^2 and y^2 are divided by -2y.

Multiply by -2y:

x = (x^2+y^2)/-2y
-2xy = x^2 + y^2
x^2 + 2xy + y^2 = 0

That should look familiar, it's a perfect square.

(x + y)^2 = 0

x = -y

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(3) (2x^3-x^2-6x) / (2x+3)

If you factor the numerator, you'll probably get a 2x+3 that you can cancel out:

x (2x^2 - x - 6) / (2x + 3)
x (2x + 3) (x - 2) / (2x + 3)
x (x - 2)
x^2 - 2x

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(4)

x^2 + 2xy + y^2 = 121

Again, you have to recognize the square of the sum of x and y:

(x + y)^2 = 121
x + y = +/- 11

There are two solutions, x + y = 11 and x + y = -11.

However, you are also given that x and y are both positive. Two positive numbers can't add up to -11, so that solution is eliminated. The one remaining solution is:

x + y = 11
or
y = 11 - x

Answer 2

Factorizing, we have
sqrt( (6x + 2y)^2 ) = sqrt( (3x + 9y)^2 )
6x + 2y = 3x + 9y [I don't think need to consider + and - here]
3x = 7y
y = (3/7)x
[Is a negative sign missing in the question?]

(did u omit the brackets?)
x = (x^2 + y^2)/(-2y)
x^2 + 2xy + y^2 = 0
(x+y)^2 = 0
x+y = 0
y = -x

My method is similar to long division, but I called it by "force".
Express 2x^3-x^2-6x as (2x+3)(...)
To get 2x^3, multiply 2x by x^2, thus (2x+3)(x^2...), which is 2x^3 + 3x^2 ...
To get -x^2, need get a -4x^2 to be subtracted from 3x^2, thus (2x+3)(x^2-2x...) because 2x*(-2x) = -4x^2.
Now (2x+3)(x^2-2x...) = 2x^3 - x^2 - 6x, which happens to be the numerator.
Thus,
(2x+3)(x^2-2x) / (2x+3) = x^2 - 2x.
Ooops, where is the equation???

x^2 + 2xy + y^2 = 121
(x + y)^2 = 121
x + y = 11 or -11 (N.A. since x and y both positive)
y = 11-x

Answer 3

Some help with the first problem. Need some background! The square root of 49 is 7 because 49 is 7x7. So, the square root of 49 is the square root of 7x7. The answer is one of the sevens.

You factor the first expression to get the square root of (6x+2y))(6x+2y). and the second expression factors to (3x+9y)(3x+9y). Taking the square root of each side you get 6x+2y=3x+9y. From here, you can solve for y.

Answer 4

sqr[36x^2 + 24xy + 4y^2] = sqr[9x^2 + 54xy + 81y^2]
Square both sides
36x^2 + 24xy + 4y^2 = 9x^2 + 4xy + 81y^2
27x^2 + 20xy - 78y^2 = 0
Divide out by y^2:
27(x/y)^2 + 20(x/y) - 78 = 0
Let z = x/y
z = {-20 +- sqr[20^2 - 4(27)(-78)]}/2(27)
= {-20 +- sqr[400 + 8424]}/54
= { -20 +- sqr[8824]}/54 = {-20 +- 2sqr[2206]}/54
= { -10 +- sqr[2206]}/27 = x/y

Answer 5

The sq. brackets mean you remedy each and every little thing contained in the brackets first and then multiply for the time of by ability of two.5-0.6 = a million.9 a million.9 [a million/7.a million^3)-(a million/9.5^4)] - regulations of indicies you swap the huge form over to get a valuable means so now its a million/the huge form to the valuable 3 and four).

Answer 6

sqrt (36x^2+24xy+4y^2)
= sqrt (6x + 2)(6x +2) )
= +or - (6x + 2)