Question

Найдите значение выражения:

                        
 (a+2b)²/2(a-4b) + (a-2b)²/3(4b-a) - 6ab+b²/2(a-4b) 
при a=-7/6,b=1/6

Answer 1

$frac{(a+2b) ^{2} }{2(a-4b)}+ frac{(a-2b) ^{2} }{3(4b-a)}- frac{6ab+b ^{2} }{2(a-4b)}= \ = frac{(a+2b) ^{2} }{2(a-4b)}- frac{(a-2b) ^{2} }{3(a-4b)}- frac{6ab+b ^{2} }{2(a-4b)}= \ = frac{3(a+2b) ^{2}-2(a-2b) ^{2}-3(6ab+b ^{2})}{6(a-4b)}= \ =frac{3a ^{2}+12ab+4b ^{2} -2a^{2}+4ab-4b ^{2}-18ab-3b ^{2})}{6(a-4b)}=$$=frac{a ^{2}-2ab-3b ^{2}}{6(a-4b)} [/tex<span>] при a=-7/6, b=1/6 получаем [tex] frac{(- frac{7}{6}) ^{2}-2cdot(- frac{7}{6})( frac{1}{6})-3cdot( frac{1}{6}) {2}}{6(- frac{7}{6}-4cdot frac{1}{6} ) }= frac{ frac{49}{46}+ frac{14}{36}- frac{3}{36}}{6cdot(- frac{11}{6}) } = frac{ frac{60}{36} }{-11} =- frac{10}{66}=- frac{5}{33}$