a)

\(C=\dfrac{3}{\sqrt{2}-1}-\dfrac{14}{3+\sqrt{2}}\\ =\dfrac{3\left(\sqrt{2}+1\right)}{2-1}-\dfrac{14\left(3-\sqrt{2}\right)}{9-2}\\ =3\sqrt{2}+3-\dfrac{14\left(3-\sqrt{2}\right)}{7}\\ =3\sqrt{2}+3-2\left(3-\sqrt{2}\right)\\ =3\sqrt{2}+3-6+2\sqrt{2}\\ =5\sqrt{2}-3\)

b)

\(\dfrac{4}{\sqrt{11}-3}-\dfrac{7}{2+\sqrt{11}}\\ =\dfrac{4\left(\sqrt{11}+3\right)}{11-9}-\dfrac{7\left(2-\sqrt{11}\right)}{4-11}\\ =\dfrac{4\left(\sqrt{11}+3\right)}{2}-\dfrac{7\left(2-\sqrt{11}\right)}{-7}\\ =2\left(\sqrt{11}+3\right)+2-\sqrt{11}\\ =2\sqrt{11}+6+2-\sqrt{11}\\ =\sqrt{11}+8\)

c)

\(B=\dfrac{1}{\sqrt{5}-2}-\dfrac{8}{\sqrt{5}+1}\\ =\dfrac{\sqrt{5}+2}{5-4}-\dfrac{8\left(\sqrt{5}-1\right)}{5-1}\\ =\sqrt{5}+2-\dfrac{8\left(\sqrt{5}-1\right)}{4}\\ =\sqrt{5}+2-2\left(\sqrt{5}-1\right)\\ =\sqrt{5}+2-2\sqrt{5}+2\\ =-\sqrt{5}+4\)

d)

\(M=\dfrac{11}{4-\sqrt{5}}-\dfrac{5+\sqrt{5}}{\sqrt{5}+1}\\ =\dfrac{11\left(4+\sqrt{5}\right)}{16-5}-\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}+1}\\ =\dfrac{11\left(4+\sqrt{5}\right)}{11}-\sqrt{5}\\ =4+\sqrt{5}-\sqrt{5}\\ =4\)

1)

\(\sqrt{6+2\sqrt{5}}\\ =\sqrt{5+2\sqrt{5}+1}\\ =\sqrt{\left(\sqrt{5}+1\right)^2}\\ =\left|\sqrt{5}+1\right|\)

\(=\sqrt{5}+1\) (\(\sqrt{5}+1>0\) )

3)

\(\sqrt{15-6\sqrt{6}}-\sqrt{10-4\sqrt{6}}\\ =\sqrt{9-6\sqrt{6}+6}-\sqrt{6-4\sqrt{6}+4}\\ =\sqrt{\left(3-\sqrt{6}\right)^2}-\sqrt{\left(\sqrt{6}-2\right)^2}\\ =\left|3-\sqrt{6}\right|-\left|\sqrt{6}-2\right|\)

\(=3-\sqrt{6}-\left(\sqrt{6}-2\right)\) (vì \(3-\sqrt{6}>0;\sqrt{6}-2>0\) )

\(=3-\sqrt{6}-\sqrt{6}+2\\ =5-2\sqrt{6}\)

5)

\(\sqrt{31-10\sqrt{6}}-\sqrt{\left(3-2\sqrt{6}\right)^2}\\ =\sqrt{25-10\sqrt{6}+6}-\left|3-2\sqrt{6}\right|\)

\(=\sqrt{\left(5-\sqrt{6}\right)^2}-\left(2\sqrt{6}-3\right)\) (vì \(3-2\sqrt{6}< 0\) )

\(=\left|5-\sqrt{6}\right|-2\sqrt{6}+3\) 

\(=5-\sqrt{6}-2\sqrt{6}+3\) (vì \(5-\sqrt{6}>0\) )

\(=8-3\sqrt{6}\)

đề yêu cầu gì ạ

`x^3 +8y^3`

`=(x+2y)(x^2 -2xy+4y^2)`

`=10*(x^2 +4xy+4y^2 -6xy)`

`=10*[(x+2y)^2 -6xy)`

`=10*(10^2 -6*(-6))`

`=10*(100+36)`

`=10*136`

`=1360`

`(x+1)+(x+2)+(x+3)+...+(x+9)=945`

`x+1+x+2+x+3+...+x+9=945`

`9x+(1+9)+(2+8)+(3+7)+(4+6)+5=945`

`9x+10+10+10+10+5=945`

`9x+45=945`

`9x=945-45`

`9x=900`

`x=900:9`

`x=100`

`2x-3y-z` hay `2x+3y-z` ạ?

tổng số tiền khi bán xe đạp là

`8xx125=1000` (xe đạp)

tổng số tiền bán xe máy là

`4216-1000=3216` (triệu đồng)

giá của mỗi xe máy là

`3216:201=16` (triệu)

nhầm tí cảm ơn đã nhắc=))

nhiều kiến thức quá nên bị lú=))

a)

\(x^2-4\sqrt{15}x+19=0\\ < =>x^2-4\sqrt{15}x+60-41=0\\ < =>\left(x-2\sqrt{15}\right)^2-41=0\\ < =>\left(x-2\sqrt{15}-\sqrt{41}\right)\left(x-2\sqrt{15}+\sqrt{41}\right)=0\\ < =>\left[{}\begin{matrix}x-2\sqrt{15}-\sqrt{41}=0\\x-2\sqrt{15}+\sqrt{41}=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=2\sqrt{15}+\sqrt{41}\\x=2\sqrt{15}-\sqrt{41}\end{matrix}\right.\)

b)

\(4x^2+4\sqrt{5}x+5=0\\ < =>\left(2x+\sqrt{5}\right)^2=0\\ < =>2x+\sqrt{5}=0\\ < =>2x=-\sqrt{5}\\ < =>-\dfrac{\sqrt{5}}{2}\)