Đáp án + Giải thích các bước giải:
`1`
`a)85^2-15^2=(85-15)(85+15)`
`=70.100=7000`
`b)73^2-13^2-10^2+20.13`
`=73^2-(13^2-2.10.13+10^2)`
`=73^2-(13-10)^2`
`=73^2-3^2=(73-3)(73+3)`
`=70.76=5320`
`c)96^3+12.96^2+3.96.16+64`
`=96^3+3.96^2.4+3.96.4^2+4^3`
`=(96+4)^3=100^3=1000000`
`d)(96^3+86^3)/(182)-96.86`
`=((96+86)(96^2-96.86+86^2))/(182)-96.86`
`=(182(96^2-96.86+86^2))/(182)-96.86`
`=96^2-96.86+86^2-96.86`
`=96^2-2.96.86+86^2`
`=(96-86)^2=10^2=100`
`2`
`a)x^2+6x+8=x^2+2x+4x+8`
`=x(x+2)+4(x+2)`
`=(x+2)(x+4)`
`b)x^2+10x+16`
`=x^2+2x+8x+16`
`=x(x+2)+8(x+2)`
`=(x+2)(x+8)`
`c)9x^2-24x+15`
`=9x^2-9x-15x+15`
`=9x(x-1)-15(x-1)`
`=(x-1)(9x-15)`
`d)x^2+4xy+3y^2`
`=x^2+xy+3xy+3y^2`
`=x(x+y)+3y(x+y)`
`=(x+y)(x+3y)`
`3`
`a)(x-3)^2=(5-2x)^2`
`⇔(x-3)^2-(5-2x)^2=0`
`⇔(x-3-5+2x)(x-3+5-2x)=0`
`⇔(3x-8)(-x+2)=0`
\(⇔\left[ \begin{array}{l}3x-8=0\\-x+2=0\end{array} \right.\)
\(⇔\left[ \begin{array}{l}x=\dfrac{8}{3}\\x=2\end{array} \right.\)
`b)1-9x^2=(3x+1)^2`
`⇔(1-3x)(3x+1)-(3x+1)^2=0`
`⇔(3x+1)(1-3x-3x-1)=0`
`⇔(3x+1)(9x)=0`
\(⇔\left[ \begin{array}{l}3x-1=0\\9x=0\end{array} \right.\)
`\(⇔\left[ \begin{array}{l}x=\dfrac{1}{3}\\x=0\end{array} \right.\)
`c)x^3+3/2 x^2+3/4 x=7/8(x>=0)`
`d)27x^3-54x^2+36x=9(x>=0)`
`⇔27x^3-54x^2+36x-9=0`
`⇔9(3x^3-6x^2+4x-1)=0`
`⇔9(3x^3-3x^2-3x^2+3x+x-1)=0`
`⇔9[3x^2(x-1)-3x(x-1)+(x-1)]=0`
`⇔9(x-1)(3x^2-3x+1)=0`
`⇔x-1=0`
`⇔x=1`
`e)(x-4)(x^2+1)+2x=8(x>=0)`
`⇔x^3-4x^2+x-4+2x=8`
`⇔x^3-4x^2+3x-12=0`
`⇔x^2(x-4)+3(x-4)=0`
`⇔(x-4)(x^2+3)=0`
`⇔x-4=0`
`⇔x=4`
