thiếu 92>0 kìa

Δ>0 thì phương trình mới có 2 nghiệm

`4x+2x(x+1)=(2x-1)^2`

`<=>4x+2x^2 +2x=4x^2 -4x+1`

`<=>4x+2x^2 +2x-4x^2 +4x-1=0`

`<=>-2x^2 +10x-1=0`

`<=>2x^2 -10x+1=0`

Ta có: `Δ=(-10)^2 -4*1*2=92>0`

\(=>\left[{}\begin{matrix}x_1=\dfrac{-\left(-10\right)+\sqrt{92}}{2\cdot2}=\dfrac{5+\sqrt{23}}{2}\\x_2=\dfrac{-\left(-10\right)-\sqrt{92}}{2\cdot2}=\dfrac{5-\sqrt{23}}{2}\end{matrix}\right.\)

Thế là dở òi=)

`A=x^2 -4x+18`

`=x^2 -4x+4+14`

`=(x-2)^2 +14`

Có `(x-2)^2 >=0 AAx`

`=> (x-2)^2 +14>= 14>0 AAx`

Vậy ....

`B=x^2 -x+2`

`=x^2 -x+1/4+7/4`

`=(x-1/2)^2 +7/4`

có `(x-1/2)^2 >=0 AAx`

`=> (x-1/2)^2 +7/4>=7/4>0 AAx`

Vậy ...........

`C=x^2 +2y^2 -2xy-2y+15`

`=x^2 -2xy+y^2 +y^2 -2y+1+14`

`=(x-y)^2 +(y-1)^2 +14`

Có `(x-y)^2 >=0 AAx,y` ;   `(y-1)^2 >=0 AAy`

`=>(x-y)^2 +(y-1)^2 +14 >=14>0 AAx;y`

Vậy

`276+x-327=458xx2`

`276+x-327=916`

`276+x=916+327`

`276+x=1243`

`x=1243-276`

`x=967`

cfs 165

ủa có luôn hả=)

`(x-2):(x-1)=(x+4)(x+7)`

\(< =>\dfrac{x-2}{x-1}=\dfrac{x+4}{x+7}\left(x\ne1;x\ne-7\right)\)

`=>(x-2)(x+7)=(x+4)(x-1)`

`<=>x^2 +7x-2x-14=x^2 -x+4x-4`

`<=>x^2 +5x-14-x^2 -3x+4=0`

`<=>2x-10=0`

`<=>2x=10`

`<=>x=5(tm)`

c)

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

\(=\left(\sqrt{18}+\sqrt{6}-2\sqrt{6}-2\sqrt{2}\right)\cdot\dfrac{\sqrt{4+2\sqrt{3}}}{\sqrt{2}}\)

\(=\left(\sqrt{18}-\sqrt{6}-2\sqrt{2}\right)\cdot\dfrac{\sqrt{3+2\sqrt{3}+1}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{2}\left(\sqrt{9}-\sqrt{3}-2\right)\sqrt{\left(\sqrt{3}+1\right)^2}}{\sqrt{2}}\)

\(=\left(3-\sqrt{3}-2\right)\left|\sqrt{3}+1\right|\)

\(=\left(1-\sqrt{3}\right)\left(\sqrt{3}+1\right)\) ( vì \(\sqrt{3}+1>0\) )

`=1-3`

`=-2`