Question

Calculati (a+b+c) - (a-b+c), unde:

a= √112 - 6√7 - √108 + 5√3
b= √175 - 6√7 - 6√3 + √192
c= √75 - 8√7 - 6√3 + √112

Answer 1

$\displaystyle (a+b+c)-(a-b+c)= \\ \\ =a+b+c-a+b-c= \\ \\ =2b= \\ \\ =2 \sqrt{175}-12 \sqrt{7}-12 \sqrt{3}+2 \sqrt{192}= \\ \\ =2 \cdot \sqrt{25 \cdot 7 }-12 \sqrt{7}-12\sqrt{3} +2 \sqrt{64 \cdot 3}= \\ \\ =2 \cdot 5 \sqrt{7}-12 \sqrt{7}-12 \sqrt{3}+2 \cdot 8 \sqrt{3}= \\ \\ =10 \sqrt{7}-12 \sqrt{7}-12 \sqrt{3}+16 \sqrt{3}= \\ \\ =-2 \sqrt{7}+4 \sqrt{3}$

Answer 2

a=-2√7-√3
b=-√7+2√3
c=-√3-4√7
(a+b+c)-(a-b+c)=
(-2√7-√3-√7+2√3-√3-4√7)-[-2√7-√3-(-√7+2√3)-√3-4√7]
-2√7+4√3
2(-√7+2√3)