(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For the following irrational equation

[tex]x^2 + 7x + 10 + \sqrt{x^2 + 7x + 12} = 0[/tex]

Find all possible unknown of X.

2. Relevant equations

None. Just your ability to solve equations.

3. The attempt at a solution

First of all, I am not allowed to use a calculator to solve this (During an exam).

Second of all, I am not sure why this is considered as irrational equation, but I went ahead and attempted to solve it.

[tex]x^2+7x+10 = -\sqrt{x^2+7x+12}[/tex]

[tex]x^2+7x+10 = -\sqrt{(x+4)(x+3)}[/tex]

[tex](x^2+7x+10)^2 = (x+4)(x+3)[/tex]

[tex]x^4+14x^3+140x + 69x^2 + 100 = x^2 + 7x + 12[/tex]

[tex]x^4 + 14x^3 + 68x^2 + 133x + 88 = 0[/tex]

And I am completely stuck here. I know no method which you can solve this fourth order equation by hand (Remember, NO CALCULATORS TO SOLVE THIS)

Any ideas?

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# Homework Help: Finding the unknowns of irrational equation

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