Question

punctul c va rogggggg​

Answer 1

Răspuns:

= 0

Explicație pas cu pas:

c) √(30-12√6) - 3√2 + 2√3 ∈ N ?

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√(30-12√6) = √(3√2 - 2√3)² = I 3√2 - 2√3 I

(3√2 - 2√3)² = 9·2 - 2·3√2·2√3 + 4·3 = 18 + 12 - 12√6

= 30 - 12√6

I 3√2 - 2√3 I = I√18 - √12I = √18 - √12 = 3√2 - 2√3 =>

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√(30-12√6) - 3√2 + 2√3 = 3√2 - 2√3 - 3√2 + 2√3 = 0 ∈ N

Answer 2

Explicație pas cu pas:

$\sqrt{30 - 12 \sqrt{6} } - 3 \sqrt{2} + 2 \sqrt{3} =$

$= \sqrt{18 - 2 \cdot 3\sqrt{2} \cdot 2 \sqrt{3} + 12} - 3 \sqrt{2} + 2 \sqrt{3}$

$= \sqrt{ {(3 \sqrt{2})}^{2} - 2 \cdot 3\sqrt{2} \cdot 2 \sqrt{3} + {(2 \sqrt{3})}^{2} } - 3 \sqrt{2} + 2 \sqrt{3}$

$= \sqrt{ {(3 \sqrt{2} - 2 \sqrt{3})}^{2} } - 3 \sqrt{2} + 2 \sqrt{3}$

$= |3 \sqrt{2} - 2 \sqrt{3}| - 3 \sqrt{2} + 2 \sqrt{3}$

$= 3 \sqrt{2} - 2 \sqrt{3} - 3 \sqrt{2} + 2 \sqrt{3} = \bf 0\in \mathbb{N}$

.

$3 \sqrt{2} > 2 \sqrt{3} \implies |3 \sqrt{2} - 2 \sqrt{3}| = 3 \sqrt{2} - 2 \sqrt{3}$