Question

(2√3 + 1 ) ( 2 + √3 ) - (√6 + √ 2)^2 С полным объяснением, не просто ответ. Заранее спасибо

Answer 1

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Answer 2

(2√3 + 1 ) ( 2 + √3 ) - (√6 + √ 2)^2 = 4√3+6+2+√3-6-2√12-2=5√3-2√12=5√3-2√(4*3)=5√3-4√3=√3

Answer 3

Calculating the Expression (2√3 + 1) / (2 + √3) - (√6 + √2)^2

To calculate the given expression (2√3 + 1) / (2 + √3) - (√6 + √2)^2, we'll break it down step by step.

1. Calculate (2√3 + 1) / (2 + √3): - To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is (2 - √3). - This gives us: \[ \frac{{(2\sqrt{3} + 1) \cdot (2 - \sqrt{3})}}{{(2 + \sqrt{3}) \cdot (2 - \sqrt{3})}} \] - After simplifying, we get: \[ \frac{{4\sqrt{3} - 2 + 2 - \sqrt{3}}}{{4 - 3}} \] - This further simplifies to: \[ \frac{{3\sqrt{3}}}{{1}} \] - Therefore, (2√3 + 1) / (2 + √3) = 3√3

2. Calculate (√6 + √2)^2: - To calculate this, we first square the binomial: \[ (\sqrt{6} + \sqrt{2})^2 = 6 + 2\sqrt{12} + 2 \] - Simplifying further, we get: \[ 8 + 2\sqrt{12} \] - Since \(\sqrt{12} = 2\sqrt{3}\), the expression becomes: \[ 8 + 4\sqrt{3} \]

3. Substitute the values back into the original expression: - Now, we substitute the calculated values back into the original expression: \[ 3\sqrt{3} - (8 + 4\sqrt{3}) \] - Simplifying this, we get: \[ 3\sqrt{3} - 8 - 4\sqrt{3} \] - Combining like terms, we get the final result: \[ -8 - \sqrt{3} \]

Therefore, the value of the given expression (2√3 + 1) / (2 + √3) - (√6 + √2)^2 is -8 - √3.