17) \(\left(4x+3\right)^2-16x\left(x+6\right)+7\left(10x+1\right)=0\)
\(\Leftrightarrow16x^2+12x+9-16x^2-96x+70x+7=0\)
\(\Leftrightarrow-14x+16=0\)
\(\Leftrightarrow14x=16\)
\(\Leftrightarrow x=\dfrac{8}{7}\)
b) \(\left(9-2x\right)^2-4\left(x-3\right)^2=81-24x\)
\(\Leftrightarrow\left(9-2x\right)^2-\left[2\left(x-3\right)\right]^2-81+24x=0\)
\(\Leftrightarrow\left(9-2x+2x-6\right)\left(9-2x-2x+6\right)-81+24x=0\)
\(\Leftrightarrow3\left(15-4x\right)-81-24x=0\)
\(\Leftrightarrow45-12x-81-24x=0\)
\(\Leftrightarrow36x=-36\)
\(\Leftrightarrow x=-1\)
c) \(\left(2x-7\right)^2-4\left(x-9\right)\left(x+9\right)-12x-13=0\)
\(\Leftrightarrow\left(2x-7\right)^2-4\left(x^2-81\right)-12x-13=0\)
\(\Leftrightarrow\left(2x-7\right)^2-4x^2+324-12x-13=0\)
\(\Leftrightarrow\left(2x-7-2x\right)\left(2x-7+2x\right)-12x+311=0\)
\(\Leftrightarrow-7\left(4x-7\right)-12x+311=0\)
\(\Leftrightarrow-28x+49-12x+311=0\)
\(\Leftrightarrow40x=360\)
\(\Leftrightarrow x=9\)
d) \(\left(x-1\right)^2-6\left(x-1\right)\left(x+1\right)=-9\)
\(\Leftrightarrow x^2-2x+1-6\left(x^2-1\right)+9=0\)
\(\Leftrightarrow x^2-2x+1-6x^2+6+9=0\)
\(\Leftrightarrow-5x^2-2x+16=0\)
\(\Leftrightarrow-5x^2-10x+8x+16=0\)
\(\Leftrightarrow-5x\left(x+2\right)+8\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(-5x+8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\-5x+8=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{8}{5}\end{matrix}\right.\)
21:
a: \(A-B=x^2+1-2x+3\)
\(=x^2-2x+4\)
\(=\left(x-1\right)^2+3>=3>0\forall x\)
=>A>B
b: \(A-B=x^2+x-2-\left(-3x^2+9x-16\right)\)
\(=x^2+x-2+3x^2-9x+16\)
\(=4x^2-8x+14\)
\(=4x^2-8x+4+10\)
\(=\left(2x-2\right)^2+10>=10>0\forall x\)
=>A>B
23:
a: \(x^2+y^2+z^2=xy+yz+xz\)
=>\(2x^2+2y^2+2z^2=2xy+2yz+2xz\)
=>\(\left(x^2-2xy+y^2\right)+\left(y^2-2yz+z^2\right)+\left(x^2-2xz+z^2\right)=0\)
=>\(\left(x-y\right)^2+\left(y-z\right)^2+\left(x-z\right)^2=0\)
=>x=y=z
`18)`
`a)VT=(a+b+c)^2`
`=(a+b)^2 +2(a+b).c+c^2`
`=a^2 +2ab+ b^2 +2ca + 2bc +c^2`
`=a^2 +b^2 +c^2 +2ab+2bc+2ca=VP`
`b)VT=(a-b+c)^2`
`=(a-b)^2 +2(a-b).c+c^2`
`=a^2 -2ab+b^2 +2ca-2bc+c^2`
`=a^2 +b^2 +c^2-2ab-2bc+2ca=VP`
