M=$\sqrt{\frac{2}{3}}$ -$\sqrt{54}$ + $\frac{2}{√6-1}$
=$\frac{√6}{3}$ -3√6 + $\frac{2+2√6}{5}$
=$\frac{5√6-45√6+6+6√6}{15}$
= $\frac{-34√6+ 6}{15}$
2,
a,N=($\frac{√a+a}{√a+1}$ +1)(1-$\frac{a-√a}{√a-1}$ ):$\frac{1-√a}{1+√a}$
=($\frac{√a+a+√a+1}{√a+1}$)( $\frac{2√a-a-1}{√a-1}$ ).$\frac{1+√a}{1-√a}$
=($\frac{(√a+1)^2}{√a+1}$ )($\frac{√a+√a-a-1}{√a-1}$ ).$\frac{1+√a}{1-√a}$
=√a+1( $\frac{-√a(√a-1)+(√a-1)}{√a-1}$ ).$\frac{1+√a}{1-√a}$
=(√a+1)(-√a+1).$\frac{1+√a}{1-√a}$
=(-a+√a - √a+1).$\frac{1+√a}{1-√a}$
=(1-a).$\frac{1+√a}{1-√a}$
=(1+√a)^2=1+2√a+a
b, Khi a=27+10√2 thì
N=1+2$\sqrt{27+10√2}$ +27+10√2
= 38+12√2
Vậy khi a=27+10√2 thì N=38+12√2
Chúc bạn học tốt !!
