(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: (1+3−3)⋅3−3(1+3−3)⋅2+2(1+3−3)−1\left(1 + 3 - \sqrt{3}\right) \cdot 3 - 3 \left(1 + 3 - \sqrt{3}\right) \cdot 2 + 2 \left(1 + 3 - \sqrt{3}\right) - 1

MathBot Answer:

(1+3−3)⋅3−3(1+3−3)⋅2+2(1+3−3)−1=−5+3≈−3.26794919243112270647255365849413\left(1 + 3 - \sqrt{3}\right) \cdot 3 - 3 \left(1 + 3 - \sqrt{3}\right) \cdot 2 + 2 \left(1 + 3 - \sqrt{3}\right) - 1 = -5 + \sqrt{3} \approx -3.26794919243112270647255365849413

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