`sqrt{10+5sqrt3}>sqrt{10-5sqrt3}`

`=>sqrt{10+5sqrt3}-sqrt{10-5sqrt3}>0`

`=>A>0`

`A=sqrt{10+5sqrt3}-sqrt{10-5sqrt3}`

`<=>A^2=10+5sqrt3+10-5sqrt3-2sqrt{(10+5sqrt3)(10-5sqrt3)}`

`<=>A^2=20-2sqrt{100-75}=20-2sqrt{25}`

`<=>A^2=20-2.5=10`

`<=>A=sqrt10`(do `A>0`)

`4b^2+a^2+4ab`

`=(2b)^2+2.2b.a+a^2`

`=(a+2b)^2`

`-49-2a^4+14sqrt2a^2`

`=-(2a^4-14sqrt2a^2+49)`

`=-((sqrt2a^2)^2-2.sqrt2a^2.7+7^2)`

`=-(sqrt2a^2-7)^2`

$\rm Cho\ a,b,c \ge 0 .Thoả \ mãn \ ab+bc+ac=abc .Chứng \ minh\ a^{2}+b^{2}+c^{2}+5abc \ge 8$

`b)` Cho` a,b,c>=0,ab+bc+ca+abc=4`

CMR:`a^2+b^2+c^2+5abc>=8`

`A=2x^2-2xy-6x+y^2+10`

`A=x^2-2xy+y^2+x^2-6x+10`

`A=(x-y)^2+x^2-6x+9+1`

`A=(x-y)^2+(x-3)^2+1`

Vì `(x-y)^2+(x-3)^2>=0=>A>=1`

Dấu "=" xảy ra khi `{(x-y=0),(x-3=0):}<=>x=y=3`

`x^4+2x^3+5x^2+4x-12`

`=x^4-x^3+3x^3-3x^2+8x^2-8x+12x-12`

`=x^3(x-1)+3x^2(x-1)+8x(x-1)+12(x-1)`

`=(x-1)(x^3+3x^2+8x+12)`

`=(x-1)(x^3+2x^2+2x^2+4x+6x+12)`

`=(x-1)[x^2(x+2)+2x(x+2)+6(x+2)]`

`=(x-1)(x+2)(x^2+2x+6)`

`a)x(2x-1)-(x-1)^2-x^2=0`

`<=>2x^2-x-x^2+2x-1-x^2=0`

`<=>x-1=0`

`<=>x=1`

Vậy `x=1.`

`b)(x+2)^3-x^3-6x^2=4`

`<=>x^3+6x^2+12x+8-x^3-6x^2=4`

`<=>12x+8=4`

`<=>12x=-4`

`<=>x=-1/3`

Vậy `x=-1/3.`

`81^8=3^x`

`=>3^x=(3^4)^8`

`=>3^x=3^32`

`=>x=32`

Vậy `x=32`

`(6x-7)^4=625=(5)^4=(-5)^4`

`=>[(6x-7=5),(6x-7=-5):}`

`=>[(6x=12),(6x=2):}`

`=>[(x=2),(x=1/3):}`

Vậy `x=2` hoặc `x=1/3.`

`1)(x-y)(6x^2-4y^2+1/2xy)`

`=6x^3-4xy^2+1/2x^2y-6x^2y+4y^3-1/2xy^2`

`=6x^3-11/2x^2y-9/2xy^2+4y^3`

`2)(6x-1)(3+x)+(2x+5)(-3x)`

`=18+6x^2-x-3-6x^2-15x`

`=-15x+15`

`a)(2x-1)^2+(x+3)^2-5(x-7)(x+7)`

`=4x^2-4x+1+x^2+6x+9-5(x^2-49)`

`=5x^2-5x^2-4x+6x+1+9+245`

`=2x+255`

`b)(x-2)(x^2+2x+4)-(25+x^3)`

`=x^3-8-x^3-25=-33`