-m^2 (xy + 4 y^2) + m ( 4xy + 8 y^2 ) - 8xy = 0am^2 + bm + c = 0.

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- Thread starter Saumyojit
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-m^2 (xy + 4 y^2) + m ( 4xy + 8 y^2 ) - 8xy = 0am^2 + bm + c = 0.

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Now use the quadratic formula, which I already mention.-m^2 (xy + 4 y^2) + m ( 4xy + 8 y^2 ) - 8xy = 0

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m = (-b ± √(b^2 - 4ac)) / 2ado it yourself.

{ - ( 4xy + 8 y^2 ) +_ √ [ ( 4xy + 8 y^2 ) ^2 - 4* - (xy + 4y^2) * - 8xy ] } / ( 2 * (-xy - 4y^2 ) )

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This is M.m = (-b ± √(b^2 - 4ac)) / 2a

{ - ( 4xy + 8 y^2 ) +_ √ [ ( 4xy + 8 y^2 ) ^2 - 4* - (xy + 4y^2) * - 8xy ] } / ( 2 * (-xy - 4y^2 ) )

What do you need to find?

And do you remember this? The number of questions Mini answers in x min: x/M

The result should be simplified, if possible. Not sure how to eliminate one of the 2 roots. Maybe we can prove that one of them is negative.

If you don't get the right answer it's likely you made a mistake - I didn't check your calculations (please don't ask me to do it).

yes.This is M.

What do you need to find?

And do you remember this? The number of questions Mini answers in x min: x/M

x/M

If you don't get the right answer it's likely you made a mistake - I didn't check your calculations

I checked calculation once again and found it will be 8xy.{ - (8xy+ 8 y^2 ) +_ √ [ (8xy+ 8 y^2 ) ^2 - 4* - (xy + 4y^2) * - 8xy ] } / ( 2 * (-xy - 4y^2 ) )

m= { - (

x/m = x / ( { - (

Do i simplify m further?

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Then, rather than write a division, I would write x/m as x times the reciprocal.

Then, when there is a radical in the denominator, you can rationalize the denominator using the conjugate.

m= { - (I would simplify m before you divide x by m; do you see that you can factor 2y out of everything, and cancel it?

m= { -

m= { 2y ( - 4x - 4y ) +_ √ [ ( 64 x^2 y ^2 + 64 y^4 + 2 * 8xy * 8y^2 ) + ( -32x^2 y^2 - 128xy^3 ] } / ( -2xy - 8y^2 ) )

m = { 2y ( - 4x - 4y ) +_ √ [

then?

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You didn't factor 2y out of them= { - (8xy+ 8 y^2 ) +_ √ [ (8xy+ 8 y^2 ) ^2 - 4* (8x^2 y^2 + 32 xy^3) ] } / ( 2 * (-xy - 4y^2 ) )

m= { -8xy -8 y^2 ) +_ √ [ (8xy+ 8 y^2 ) ^2 - 4* (8x^2 y^2 + 32 xy^3) ] } / ( -2xy - 8y^2 ) )

m= { 2y ( - 4x - 4y ) +_ √ [ ( 64 x^2 y ^2 + 64 y^4 + 2 * 8xy * 8y^2 ) + ( -32x^2 y^2 - 128xy^3 ] } / ( -2xy - 8y^2 ) )

m = { 2y ( - 4x - 4y ) +_ √ [2y( 32 x^2 y + 32y^3 + 64x y^2 +2y( -16x^2 y - 64 xy^2 ) ] } /2y( -x -4y )

then?

I'm not reading through every detail and checking, so I can't say whether what you have is right; but this is part of the work of simplifying what you have.

I'd also multiply numerator and denominator by -1 at some point, to get rid of many negatives.

2y ( - 4x - 4y ) +_You didn't factor 2y out of theradical. Are you aware that √(4y^2 ...) = 2y √(...)? Factor 4y^2 from the radicand, and take the square root of it. Then you can divide everything by it.

2y { ( - 4x - 4y ) +_ √ ( 16x^2 + 16 y^2 + 32xy - 8x^2 + 32xy ) } / 2y ( - x - 4y )

( - 4x - 4y ) +_ √ ( 8x^2 + 16 y^2 + 64xy ) / ( - x - 4y )

( - 4x - 4y ) +_ √ ( (2x √2) ^2 + (2y √4) ^2 + 64xy ) / ( - x - 4y )

then?

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First, I see an error compared to my work (which is easier to see now that it is simplified); you could also see it by2y ( - 4x - 4y ) +_√ (4y^2 )* √( 16x^2 + 16 y^2 + 32xy - 8x^2 + 32xy ) / 2y ( -x - 4y )

2y { ( - 4x - 4y ) +_ √ ( 16x^2 + 16 y^2 + 32xy - 8x^2 + 32xy ) } / 2y ( - x - 4y )

( - 4x - 4y ) +_ √ ( 8x^2 + 16 y^2 + 64xy ) / ( - x - 4y )

( - 4x - 4y ) +_ √ ( (2x √2) ^2 + (2y √4) ^2 + 64xy ) / ( - x - 4y )

then?

So go back and look for where your

Also, your last line doesn't help make anything simpler, so drop it.

Then, I recommend the other step I mentioned, multiplying by -1/-1 to eliminate the negative signs (again, you'll see that this will make your answer closer to the choices).

And then do the final thing I've already told you to do:

This will get you to something very close to the choices; but you have to decide whether either choice in the plus-or-minus is invalid.Then, rather than write a division, I wouldwrite x/m as x times the reciprocal.

Then, when there is a radical in the denominator, you canrationalize the denominatorusing the conjugate.

{ ( - 4x - 4y ) +_ √ ( 16x^2 + 16 y^2 +** 32xy** - 8x^2 + **32xy** ) } / ( - x - 4y )

From herewhere your64xycame from

i did not find anycorrect what is probably asign error.

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Then look again,i did not find any

Have you gone through what you wrote in #69? How about the step from there to #71? You need to check every single step you write (and better as soon as you write it than later!).

Yeah , { ( - 4x - 4y ) +_ √ ( 16x^2 + 16 y^2 + 32xy - 8x^2{ ( - 4x - 4y ) +_ √ ( 16x^2 + 16 y^2 +32xy- 8x^2 +32xy) } / ( - x - 4y )

{ ( - 4x - 4y ) +_ √ ( 16x^2 + 16 y^2 - 8x^2 ) } / ( - x - 4y )

{ ( - 4x - 4y ) +_ √ ( 8x^2 + 16 y^2 ) } / ( - x - 4y )

{ ( - 4x - 4y ) +_ √ ( 8x^2 + 16 y^2 ) } / ( - x - 4y )

{ ( - 4x - 4y ) +_ √ ( 2x (√2) ^2 + ( 2y √4 ) ^2 ) } / ( - x - 4y )

m = { ( - 4x - 4y ) +_ √ ( ( √ 4 √2 √2 ) { x^2 + y^2 * √4 ) ) } / ( - x - 4y )

m= { 2 ( - 2x - 2y ) +_ 2 √2 * √ ( x^2 + 2y^2 ) / ( - x - 4y )

Taking 2 common

m=

Then? x/m

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First, look back at the choices, and you'll see that pulling √2 out of the radical doesn't help. (I wouldn't do it anyway, because it just doesn't look simpler.)Yeah , { ( - 4x - 4y ) +_ √ ( 16x^2 + 16 y^2 + 32xy - 8x^2-32xy ) } / ( - x - 4y )

{ ( - 4x - 4y ) +_ √ ( 16x^2 + 16 y^2 - 8x^2 ) } / ( - x - 4y )

{ ( - 4x - 4y ) +_ √ ( 8x^2 + 16 y^2 ) } / ( - x - 4y )

{ ( - 4x - 4y ) +_ √ ( 8x^2 + 16 y^2 ) } / ( - x - 4y )

{ ( - 4x - 4y ) +_ √ ( 2x (√2) ^2 + ( 2y √4 ) ^2 ) } / ( - x - 4y )

m = { ( - 4x - 4y ) +_ √ ( ( √ 4 √2 √2 ) { x^2 + y^2 * √4 ) ) } / ( - x - 4y )

m= { 2 ( - 2x - 2y ) +_ 2 √2 * √ ( x^2 + 2y^2 ) / ( - x - 4y )

Taking 2 common

m=2{ ( - 2x - 2y ) +_ √2 * √ ( x^2 + 2y^2 ) } / ( - x - 4y )

Then? x/m

Then ...

Just keep doing what I've already said to do!

Then, I recommend the other step I mentioned,multiplying by -1/-1to eliminate the negative signs (again, you'll see that this will make your answer closer to the choices).

And then do the final thing I've already told you to do:

If you don't understand, ask specifically about it, rather than acting like we've never told you anything.... write x/m asx times the reciprocal.

Then, when there is a radical in the denominator, you canrationalize the denominatorusing the conjugate.

Answer has come taking negative part of (b^2 - 4ac) ^1/2...First, look back at the choices, and you'll see that pulling √2 out of the radical doesn't help.

If you don't understand, ask specifically about it, rather than acting like we've never told you anything.

1/4[ 2 ( x+y)

its finally done .

pulling √2 out of the radical doesn't help , multiplying by -1/-1 and rationalize the denominator using the conjugate are 2 most important steps .

How did you understand that pulling √2 out of the radical doesn't help?

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I will ask you again: Have you looked at the choices given in the problem lately?Q.

Mini and Vinay are quiz masters preparing for a quiz. In 'x' minutes, Mini makes 'y' questions more than Vinay. If it were possible to reduce the time needed by each to make a question by 2 mins , then in 'x' minutes Mini would make '2y' questions more than Vinay. How many questions does Mini make in 'x' minutes?

1] 1/4[ 2 ( x+y) - ( 2 x^2 + 4 y^2 )^1/2 ]

2] 1/4[ 2(x-y) - ( 2 x^2 + 4 y^2 )^1/2 ]

3] Either option 1 or 2

4] 1/4[ 2(x-y) - ( 2 x^2 - 4 y^2 )^1/2 ]