\(a,\left(x-2\right)^3-\left(x-9\right)^3=21\left(x-8\right)^2\\\Leftrightarrow \left[\left(x-2\right)-\left(x-9\right)\right].\left[\left(x-2\right)^2+2.\left(x-2\right)\left(x-9\right)+\left(x-9\right)^2\right]=21\left(x^2-16x+64\right)\\ \Leftrightarrow7\left(x^2-4x+4+2x^2-22x+36+x^2-18x+81\right)=21x^2-336x+1344\\ \Leftrightarrow28x^2-308x+847-21x^2+336x-1344=0\\ \Leftrightarrow7x^2+28x-497=0\\ \Leftrightarrow x^2+4x-71=0\\ \Leftrightarrow\left(x+2-5\sqrt{3}\right)\left(x+2+5\sqrt{3}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+2-5\sqrt{3}=0\\x+2+5\sqrt{3}=0\end{matrix}\right.\\ \Leftrightarrow x=-2\pm5\sqrt{3}\)
\(b,\left(5x-6\right)^2-\left(3x-7\right)^2=-9x\left(x-8\right)+\left(5x-6\right)^2-13\\ \Leftrightarrow\left(25x^2-60x+36\right)-\left(9x^2-42x+49\right)=-9x^2+72+25x^2-60x+36-13\\ \Leftrightarrow25x^2-9x^2+9x^2-25x^2-60x+42x+60x=72+36-13+49-36\\ \Leftrightarrow42x=144\\ \Leftrightarrow x=\dfrac{144}{42}=\dfrac{24}{7}\)
