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## #1 2006-04-05 19:38:45

4littlepiggiesmom
Member
Registered: 2006-01-09
Posts: 42

### Solving Equations then tell which solution method you used!

T^2 -16T +65=0

Factoring  and Graphin but  65 only factors are
1 *65  and
5*13???
Any one have any ideas??? Please??? Mom's lost...and My son had left this problem after working on it for over an hour! Thanks Mom

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## #2 2006-04-05 20:24:35

gnitsuk
Member
Registered: 2006-02-09
Posts: 121

### Re: Solving Equations then tell which solution method you used!

This equation has no real solutions. The quadratic formula gives T = [-b +- sqrt(b^2 - 4ac)] / 2a here we have a = 1, b = -16 and c = 65 putting these values in we get:

T = [16 +- sqrt(-4)] / 2 = [16 +- 2*sqrt(-1)] / 2 = 8 +- sqrt(-1) = 8 +- i

So the solutions are:

T = 8 + i

and

T = 8 - i

If you plug these into the initial equation you will see that they satisfy it. Let's just do the first one:

T = 8 + i =>

T^2 = (8 + i)*(8 + i) = 64 - 16i -1 = 63 + 16i

Substituting into the LHS of the original equation yields:

63 + 16i - 128 - 16i + 65 which is clearly zero. Similarly for T = 8 - i

Last edited by gnitsuk (2006-04-05 20:25:58)

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## #3 2006-04-06 00:57:07

4littlepiggiesmom
Member
Registered: 2006-01-09
Posts: 42

### Re: Solving Equations then tell which solution method you used!

What do the i's stand for? And if the sqrt = a negative number I thought it would's you do

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## #4 2006-04-06 01:17:47

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: Solving Equations then tell which solution method you used!

By definition:

This is a complex number.

IPBLE:  Increasing Performance By Lowering Expectations.

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## #5 2006-04-09 06:33:02

Member
Registered: 2006-04-09
Posts: 1

### Re: Solving Equations then tell which solution method you used!

Can you help me solve this puzzle please.

Thirty-six minus ten=
3+3+3*3=
5*5*0=
20-15=

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## #6 2006-04-09 07:47:10

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Solving Equations then tell which solution method you used!

For future reference, make your own help topic instead of posting in someone else's.

Anyway, this is one of those puzzles that can be interpreted in so many ways that the answer that the setter of the puzzle is thinking of is probably completely different from the one that everyone else gets.

If there's no trickery, then the answer is 26+15+0+5 = 46. But I suspect there is.

Why did the vector cross the road?
It wanted to be normal.

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