Question

são dadas os números reais A, B, e C tais que 

A= 1-\sqrt{27}

B=1+ \sqrt{75}

C=2-\sqrt{108}

 Determine o valr de:a) A+B+C            b)A-B-C

Answer 1

Temos que:

 

$\text{A}=1-\sqrt{27}=1-3\sqrt{3}$

 

$\text{B}=1+\sqrt{75}=1+5\sqrt{3}$

 

$\text{C}=2-\sqrt{108}=2-6\sqrt{3}$

 

Logo:

 

$\text{A}+\text{B}+\text{C}=(1-3\sqrt{3})+(1+5\sqrt{3})+(2-6\sqrt{3})=4-4\sqrt{3}=4\cdot(1-\sqrt{3})$

 

 

$\text{A}-\text{B}-\text{C}=(1-3\sqrt{3})-(1+5\sqrt{3})-(2-6\sqrt{3})=-2-2\sqrt{3}$