Question

Выполнить 4 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))
4)Вычислите
(√196*√19.6)/(√0.196*√1.69)

Answer 1

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

2) 2a^2 - 5ab + 2b^2 = a^2 - 4ab + 4b^2 + a^2 - ab - 2b^2 = (a-2b)^2 + (a-2b)(a+b) = (a-2b)(a-2b+a+b) = (a-2b)(2a-b)

При a = √7+√6; b = √7-√6 получается:

2a^2 - 5ab + 2b^2 = (a-2b)(2a-b) = (√7+√6-2√7+2√6)(2√7+2√6-√7+√6) = (3√6-√7)(3√6+√7) = 9*6 - 7 = 54 - 7 = 47

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

4) $\frac{\sqrt{196}*\sqrt{19,6}}{\sqrt{0,196}*\sqrt{1,69}} = \frac{14*14\sqrt{0,1}}{1,4*\sqrt{0,1}*1,3} =\frac{10*14}{1,3}=\frac{1400}{13}$