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Find the solution set of three 𝑥 squared over seven equals three, that isn’t in the set of rational numbers.
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So looking at this question, we can actually see this last bit of notation.
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And I’ve just wanted to explain what that actually meant.
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And as I said when I read the question through, it means it is not in the set of rational numbers.
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And that’s because our apostrophe, that means not.
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And the capital 𝑄 means set of rational numbers.
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So therefore, we know that our solutions are gonna be irrational numbers.
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Okay, so now we can actually solve the equation.
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So we have three 𝑥 squared over seven equals three.
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So first of all, we multiply each side of the equation by seven.
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So we get three 𝑥 squared equals 21.
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And then we actually divide each side of the equation by three.
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So we’ve now got 𝑥 squared is equal to seven.
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And as we’re looking to find 𝑥, what we do now is we’re actually gonna take the square root of each side.
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So then we get 𝑥 is equal to plus or minus root seven.
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So then we take a look at the root seven part of our answer.
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Because for it to actually fulfill the set of solutions that we want, it needs to be in a rational number.
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And yes, root seven is a surd.
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And it is an irrational number.
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So great, we now know we can carry on and get the solution set.
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So therefore, we can say that the solution set of three 𝑥 squared over seven equals three, that isn’t in the set of rational numbers, is negative root seven, root seven.