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zloy xaker [14]
3 years ago
12

Find the exact solutions and simplify as much as possible: 3x^2+1=6x

Mathematics
1 answer:
svetoff [14.1K]3 years ago
5 0

Answer:

\frac{3+ \sqrt{6} }{3} and \frac{3- \sqrt{6} }{3}

Step-by-step explanation:

This is a quadratic equation, so we start by rearranging its terms so we can apply the quadratic formula:

ax^2+bx+c=0 has two possible solutions given by:

x=\frac{-b+/- \sqrt{b^2-4ac} }{2a}

So we rearrange the terms in the given quadratic equation bringing all terms to the left hhand side of the equal sign:

3x^2+1=6x\\3x^2-6x+1=0

The solutions will then be:

x=\frac{6+/- \sqrt{36-4(3)(1)} }{2(3)}=\frac{6+/- \sqrt{36-12} }{6}=\frac{6+/- \sqrt{24} }{6}=\frac{6+/- \sqrt{4*6} }{6}=\frac{6+/- 2\sqrt{6} }{6}=\frac{3+/- \sqrt{6} }{3}

Therefore the two possible answer are: \frac{3+ \sqrt{6} }{3} and \frac{3- \sqrt{6} }{3}

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