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If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of

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If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

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New post 21 Oct 2016, 07:31
1
10
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:39) correct 36% (02:09) wrong based on 112 sessions

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If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of m^2+n^2?

A. 10
B. 12
C. 15
D. 24
E. 25

* A solution will be posted in two days.

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If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

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New post 21 Oct 2016, 07:52
1
m = x + y

n= x - y

Where x= -b/2a

y= (sqrt(b^2 - 4ac))/2a

m^2+n^2 = 2(x^2 + y^2)


= 2(9/4 + 21/4)

=15

C


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Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

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New post 21 Oct 2016, 08:00
MathRevolution wrote:
If 2 roots of an equation x^2-3x-3 = 0 are m and n, what is the value of m^2+n^2?

A. 10
B. 12
C. 15
D. 24
E. 25

* A solution will be posted in two days.


With acegmat123

That's the perfect and easiest way of solving this question

With (C) hence...

PS : Good question MathRevolution ...
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Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

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New post 26 Oct 2016, 01:56
2
1
==>From x^2-3x-3=(x-m)(x-n)=x^2-(m+n)x+mn, you get m+n=3 and mn=-3. Then you get m^2+n^2=(m+n)^2-2mn=3^2-2*(-3)=15. The answer is C.

Answer: C
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Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

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New post 30 Oct 2016, 08:08
Can someone post a step by step solution pls...Kudos for this
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Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

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New post 04 Nov 2016, 00:31
1
AK125 wrote:
Can someone post a step by step solution pls...Kudos for this


Hi AK125,

x^2-3x-3=(x-m)(x-n)=x^2-(m+n)x+mn so, m-n=3 and mn=-3

Thank you.
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Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

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New post 04 Nov 2016, 15:08
It is not clear enough. I miss some step above. please any help ?
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Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

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New post 05 Nov 2016, 02:11
MathRevolution wrote:
==>From x^2-3x-3=(x-m)(x-n)=x^2-(m+n)x+mn, you get m+n=3 and mn=-3. Then you get m^2+n^2=(m+n)^2-2mn=3^2-2*(-3)=15. The answer is C.

Answer: C


I don't understand when you solve for (m^2 + n^2) and use (m+n)^2 - 2mn in its place

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Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

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New post 08 Nov 2016, 03:01
gillyelephant wrote:
MathRevolution wrote:
==>From x^2-3x-3=(x-m)(x-n)=x^2-(m+n)x+mn, you get m+n=3 and mn=-3. Then you get m^2+n^2=(m+n)^2-2mn=3^2-2*(-3)=15. The answer is C.

Answer: C


I don't understand when you solve for (m^2 + n^2) and use (m+n)^2 - 2mn in its place

Posted from my mobile device



We do know m+n which equals 3. And we know mn which is -3.

If we square (m+n) -->

(m+n)^2 = m^2 + 2mn + n^2

Plug in what we do know (green):

(3)^2 = m^2 + 2(-3) + n^2
--> 9 = m^2 - 6 + n^2
--> 15 = m^2 + n^2

Hope its clear!
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Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

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Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of &nbs [#permalink] 27 Aug 2018, 15:47
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