Question

Giải phương trình: \(x^2+(16-x\sqrt{3})^2=4(12-x)^2\)

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Answer 1

\(x^2+\left(16-x\sqrt{3}\right)^2=4\left(12-x\right)^2\)

\(\Leftrightarrow x^2+256-32\sqrt{3}x+3x^2=4\left(144-24x+x^2\right)\)

\(\Leftrightarrow4x^2-32\sqrt{3}x+256=576-96x+4x^2\)

\(\Leftrightarrow4x^2-4x^2-32\sqrt{3}x+96x+256-576=0\)

\(\Leftrightarrow\left(96-32\sqrt{3}\right)x-320=0\)

\(\Leftrightarrow\left(96-32\sqrt{3}\right)x=320\)

\(\Leftrightarrow x=\frac{320}{96-32\sqrt{3}}=\frac{15+5\sqrt{3}}{3}\)