Question

Расписать 3 примера:
1)Вычислите
1/(√7-√6)-3/(√6-√3)-4/(√7+√3)
2)Вычислите 2a²-5ab+2b²
при a=√7+√6 и b=√7-√6
3)Упростите
3√(3*(2/3))-√132+4*√(2*(1/16))

Answer 1

1)

1/(√7-√6)-3/(√6-√3)-4/(√7+√3) $\frac{1}{\sqrt{7}-\sqrt{6}} -\frac{3}{\sqrt{6}-\sqrt{3}} -\frac{4}{\sqrt{7}+\sqrt{3}} = \frac{1*(\sqrt{7}+\sqrt{6})}{(\sqrt{7}-\sqrt{6})(\sqrt{7}+\sqrt{6})} -\frac{3*(\sqrt{6}+\sqrt{3})}{(\sqrt{6}-\sqrt{3})*(\sqrt{6}+\sqrt{3})} -\frac{4*(\sqrt{7}-\sqrt{3})}{(\sqrt{7}+\sqrt{3})*((\sqrt{7}-\sqrt{3}))} = \frac{(\sqrt{7}+\sqrt{6})}{1} -\frac{3*(\sqrt{6}+\sqrt{3})}{6-3} -\frac{4*(\sqrt{7}-\sqrt{3})}{7-3} =$$\frac{(\sqrt{7}+\sqrt{6})}{1} -\frac{3*(\sqrt{6}+\sqrt{3})}{3} -\frac{4*(\sqrt{7}-\sqrt{3})}{4} = \sqrt{7} +\sqrt{6} -\sqrt{6} -\sqrt{3} -\sqrt{7} +\sqrt{3} =0$

2) 2a²-5ab+2b² при a=√7+√6 и b=√7-√6;

$2*(\sqrt{7}+\sqrt{6})^2 -5*(\sqrt{7}+\sqrt{6})(\sqrt{7}-\sqrt{6})+2*(\sqrt{7}-\sqrt{6})^2=2*(7+2\sqrt{7*6}+6) -5*(7-6)+2*(7-2\sqrt{7*6}+6)=2*(13+2\sqrt{42} )-5+2*2*(13+2\sqrt{42} )=26+4\sqrt{42} -5+26+4\sqrt{42} =52$

3) $3\sqrt{3*\frac{2}{3}} -\sqrt{132} +4*\sqrt{2*\frac{1}{16}} = 3\sqrt{2} -\sqrt{4*33} +4*\frac{1}{4}\sqrt{2} = 3\sqrt{2} -2\sqrt{33} +\sqrt{2} = 4\sqrt{2} -2\sqrt{33} = 2(2\sqrt{2} -\sqrt{33})$

Answer 2

Решение смотрите на фото