(1+3–√3)3−3(1+3–√3)2+2(1+3–√3)−1

asked by guest
on Nov 28, 2024 at 12:49 pm



You asked:

Evaluate the expression: \(\left(1 + 3 - \sqrt{3}\right) \cdot 3 - 3 \cdot \left(1 + 3 - \sqrt{3}\right) \cdot 2 + 2 \cdot \left(1 + 3 - \sqrt{3}\right) - 1\)

MathBot Answer:

\[\left(1 + 3 - \sqrt{3}\right) \cdot 3 - 3 \cdot \left(1 + 3 - \sqrt{3}\right) \cdot 2 + 2 \cdot \left(1 + 3 - \sqrt{3}\right) - 1 = -5 + \sqrt{3} \approx -3.26794919243112270647255365849413\]

\[\begin{aligned}\left(1 + 3 - \sqrt{3}\right) \cdot 3 - 3 \cdot \left(1 + 3 - \sqrt{3}\right) \cdot 2 + 2 \cdot \left(1 + 3 - \sqrt{3}\right) - 1& = \left(4 - \sqrt{3}\right) \cdot 3 - 3 \cdot \left(1 + 3 - \sqrt{3}\right) \cdot 2 + 2 \cdot \left(1 + 3 - \sqrt{3}\right) - 1\\& = \left(12 - 3 \cdot \sqrt{3}\right) - 3 \cdot \left(1 + 3 - \sqrt{3}\right) \cdot 2 + 2 \cdot \left(1 + 3 - \sqrt{3}\right) - 1\\& = \left(12 - 3 \cdot \sqrt{3}\right) - 3 \cdot \left(4 - \sqrt{3}\right) \cdot 2 + 2 \cdot \left(1 + 3 - \sqrt{3}\right) - 1\\& = \left(12 - 3 \cdot \sqrt{3}\right) - \left(12 - 3 \cdot \sqrt{3}\right) \cdot 2 + 2 \cdot \left(1 + 3 - \sqrt{3}\right) - 1\\& = \left(12 - 3 \cdot \sqrt{3}\right) - \left(24 - 6 \cdot \sqrt{3}\right) + 2 \cdot \left(1 + 3 - \sqrt{3}\right) - 1\\& = \left(12 - 3 \cdot \sqrt{3}\right) - \left(24 - 6 \cdot \sqrt{3}\right) + 2 \cdot \left(4 - \sqrt{3}\right) - 1\\& = \left(12 - 3 \cdot \sqrt{3}\right) - \left(24 - 6 \cdot \sqrt{3}\right) + \left(8 - 2 \cdot \sqrt{3}\right) - 1\\& = \left(-12 + 3 \cdot \sqrt{3}\right) + \left(8 - 2 \cdot \sqrt{3}\right) - 1\\& = \left(-4 + \sqrt{3}\right) - 1\\& = -5 + \sqrt{3}\end{aligned}\]

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