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# Algebra

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Let a and b be real numbers such that a^3 + 3ab^2 = 679 and a^3 - 3ab^2 = 673.  Find a - b.

Jan 6, 2023

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Alright, the first step is very simple

So basically subtract 6ab^2 from the first equation and you will get the second equation so 6ab^2 = 6

$$6ab^2 = 6$$

$$ab^2 = 1$$

now, you are asking for a - b

$$b^2 = 1/a$$

$$\cdot 1/b$$ on both sides

$$b = 1/ab$$

im just doing every possible thing i can do bc this is my first time seeing this so im doing it as well as you sorry

$$ab = 1/b$$ ok that might be useful

oh......

$$a^3 + 3 = 679$$

$$a^3 = 676$$

$$a \approx 8.77639$$

so b is 1/ whatever that is. Square rooted.....

its approximately 8.43883.... probably not correct, looking at the numbers. Maybe its like the square root of something?

its like $$\sqrt{71.212}$$ not exacly but close

Jan 6, 2023