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Solve by hand. Use a calculator for arithmetic but not a CAS

1. The roots of the equation x^2 + ax + b = 0 are each one less than the roots of the equation x^2 + bx + a = 0.

Find a+b

2. If the following system of equations hold, find abc

2(a+b) + ab = 16

2(b+c) + bc = 24

2(a+c) + ac = 31

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,321

hi Agnishom,

For (1)

So write

Use the given connection between the roots to find a and b.

I'm still working on (2).

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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Vieta?

I tried that but I still do not see...

3. There are two 2-digit numbers x and y such that when the digits of their arithmetic mean are reversed, their geometric mean is found.

*Last edited by Agnishom (2014-11-01 04:58:08)*

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

Agnishom wrote:

3. There are two 2-digit numbers x and y such that when the digits of their arithmetic mean are reversed, their geometric mean is found.

What is the question?

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Find x-y

The numbers are obviously 98 and 32 but I am unable to do it by hand

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

Agnishom wrote:

3. There are two 2-digit numbers x and y such that when the digits of their arithmetic mean are reversed, their geometric mean is found. Find x-y.

*Last edited by ShivamS (2014-11-01 05:53:13)*

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Awesome. Thanks

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,321

hi Agnishom,

Do you need more help with (1) ?

I'm still working on (2).

I managed to solve using elimination but the values for a, b and c are nasty so I'm looking for a neater way.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,321

Q2. I corrected my arithmetic and it came out nicely.

re-arrange equation 2

and equation 3

eliminate c

Substitute in equation 1

times by 5

So either **a = 3, b = 2 and c = 5** or **a = -7, b = -6 and c = -9**

So **abc = 30 or - 378**

Sorry I couldn't find a 'slick' way to do this that avoids solving the equations.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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That will do. Thanks

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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