`(6)/(18)+(-14)/(21)`

`=(6:6)/(18:6)-(14:7)/(21:7)`

`=(1)/(3)-(2)/(3)`

`=(1-2)/(3)=-1/3`

`x=1+2+4+...+2^{2002}+2^{2003}`

`=1+2^{1}+2^{2}+2^{3}+...+2^{2002}+2^{2003}`

`=>2x=2^{1}+2^{2}+2^{3}+2^{4}+...+2^{2003}+2^{2004}`

`=>2x-x=(2^{1}+2^{2}+2^{3}+2^{4}+...+2^{2003}+2^{2004})-(1+2^{1}+2^{2}+2^{3}+...+2^{2002}+2^{2003})`

`=>x=2^{2004}-1`

`=>x+1=2^{2004}=y` (DPCM)

`(a):\sqrt{2x-5}=\sqrt{x-1}\     (ĐK:x\ge 5/2)`

`<=>2x-5=x-1`

`<=>2x-x=5-1`

`<=>x=4(TMDK)`

Vậy `S={4}`

`(b):x^{2}-2=x-2\sqrt{x+1}\    (ĐK:x\ge -1)`

`<=>x^{2}=x+1-2.\sqrt{x+1}.1+1^{2}`

`<=>x^{2}=(\sqrt{x+1}-1)^{2}`

`<=>|x|=|\sqrt{x+1}-1|`

`=>x=\sqrt{x+1}-1\   (1)` hoặc `x=-\sqrt{x+1}+1\   (2)`

`(1)<=>x+1=\sqrt{x+1}` 

`<=>x^{2}+2x+1=x+1`    `(ĐK:x\ge -1)`

`<=>x^{2}+x=0`

`<=>x(x+1)=0`

`=>x=0` hoặc `x=-1` (TMDK)

`(2)<=>\sqrt{x+1}=1-x`

`<=>x+1=x^{2}-2x+1`  `(ĐK:1-x\ge0;x\ge -1<=>-1\le x\le 1)`

`<=>x^{2}-3x=0`

`<=>x(x-3)=0`

`=>x=0\      (TMDK)` hoặc `x=3\     (KTMDK)`

Vậy `S={0;-1}`

Tổng chiều dài và rộng là :

    `72:2=36(cm)`

Chiều rộng là :

     `36-20=16(cm)`

`x^{2}-21x+38=(x^{2}-2x)-(19x-38)`

`=x(x-2)-19(x-2)`

`=(x-2)(x-19)`

`(a):(5\sqrt{2}+\sqrt{10})/(\sqrt{5}+1)+(12)/(4-\sqrt{10})-8\sqrt{(5)/(2)}`

`=(\sqrt{25.2}+\sqrt{10})/(\sqrt{5}+1)+(12(4+\sqrt{10}))/((4+\sqrt{10})(4-\sqrt{10}))-\sqrt{(64.5)/(2)}`

`=(\sqrt{10}.(\sqrt{5}+1))/(\sqrt{5}+1)+(12(4+\sqrt{10}))/(16-10)-\sqrt{160}`

`=\sqrt{10}+2(4+\sqrt{10})-4\sqrt{10}`

`=\sqrt{10}+8+2\sqrt{10}-4\sqrt{10}`

`=8-\sqrt{10}`

`(b):(\sqrt{3}+4)/(5-2\sqrt{3})-(5\sqrt{3}-3)/(\sqrt{3})+6\sqrt{1/3}`

`=((\sqrt{3}+4)(5+2\sqrt{3}))/((5-2\sqrt{3})(5+2\sqrt{3}))-(\sqrt{3}(5-\sqrt{3}))/(\sqrt{3})+\sqrt{(36)/(3)}`

`=(26+13\sqrt{3})/(25-12)-(5-\sqrt{3})+\sqrt{12}`

`=(13(2+\sqrt{3}))/(13)-5+\sqrt{3}+2\sqrt{3}`

`=2+\sqrt{3}-5+\sqrt{3}+2\sqrt{3}`

`=4\sqrt{3}-3`

`x^{2}+4x-21=(x^{2}-3x)+(7x-21)`

`=x(x-3)+7(x-3)`

`=(x-3)(x+7)`

`(c):` Để `(d)` cắt `(d'')` thì :

`a\ne a''`

`<=>m-3\ne 1`

`<=>m\ne 4`

`(d):` Để `(d)` \(\perp\) `(d''')` thì :

`a.a'''=-1`

`<=>(m-3).(1)/(2)=-1`

`<=>m-3=(-1):(1)/(2)=-2`

`<=>m=1`

`(-300):20+5.(3x-1)=25`

`=>-15+15x-5=25`

`=>15x-20=25`

`=>15x=25+20=45`

`=>x=45/15=3`

`axx(b+c)=axxb+axxc`

`axx(b-c)=axxb-axxc`