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

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