- #1

- 1

- 0

a,b are real.

a^3-3a^2+5a-17=0 &

b^3-3b^2+5b+11=0

a+b=?

a^3-3a^2+5a-17=0 &

b^3-3b^2+5b+11=0

a+b=?

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- Thread starter sarvesh
- Start date

- #1

- 1

- 0

a,b are real.

a^3-3a^2+5a-17=0 &

b^3-3b^2+5b+11=0

a+b=?

a^3-3a^2+5a-17=0 &

b^3-3b^2+5b+11=0

a+b=?

- #2

VietDao29

Homework Helper

- 1,423

- 3

So the first thing you should do is to add both sides of the 2 equation, that'll give:

a

If a, and b are solutions to (1), and (2), they must also be the solutions to (3), right?

Now, you can try to convert the LHS of (3) to (a + b) as much as possible(this is because you need to know what a + b is).

---------------

So you have:

a

a

Then you can try to rearrange it a bit, so it'll have the form:

[tex](a + b + \alpha) * \mbox{something} = 0[/tex] (where [itex]\alpha[/itex] is some number).

From here, it's clear that: [tex]a + b + \alpha = 0 \Leftrightarrow a + b = - \alpha[/tex]

Can you go from here?

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