a)\(\left(x-5\right)^2+\left(x+3\right)^2=2\cdot\left(x-4\right)\cdot\left(x+4\right)-5x+7\)
\(\Leftrightarrow x^2-10x+25+x^2+6x+9=2\cdot\left(x^2-4^2\right)-5x+7\)\(\Leftrightarrow x^2-10x+25+x^2+6x+9=2x^2-32-5x+7\)
\(\Leftrightarrow x^2-10x+25+x^2+6x+9-2x^2+32+5x-7=0\)
\(\Leftrightarrow x+59=0\)
\(\Rightarrow x=-59\)
b)\(\left(x+3\right)\cdot\left(x-2\right)-2\cdot\left(x+1\right)^2=\left(x-3\right)^2-2x^2+4x\)
\(\Leftrightarrow x^2-2x+3x-6-2x^2-4x-2=x^2-6x+9-2x^2+4x\)
\(\Leftrightarrow x^2-2x+3x-6-2x^2-4x-2-x^2+6x-9+2x^2-4x=0\)\(\Leftrightarrow-x-17=0\)
\(\Rightarrow x=-17\)
c)\(\Leftrightarrow\left(x+1\right)^3-\left(x+2\right)\cdot\left(x-4\right)=\left(x-2\right)\cdot\left(x^2+2x+4\right)+2x^2\)\(\Leftrightarrow x^3+3x^2+3x+1-x^2+4x-2x+8=x^3-8+2x^2\)
\(\Leftrightarrow x^3+2x^2+5x+9=x^3-8+2x^2\)
\(\Leftrightarrow x^3+2x^2+5x+9-x^3+8-2x^2=0\)
\(\Leftrightarrow5x+17=0\)
\(\Rightarrow x=\frac{-17}{5}\)
d)\(\left(x-2\right)^3+\left(x-5\right)\cdot\left(x+5\right)=x\cdot\left(x^2-5x\right)-7x+3\)
\(\Leftrightarrow x^3-6x^2+12x-8+x^2-25=x^3-5x^2-7x+3\)
\(\Leftrightarrow19x-36=0\)
\(\Rightarrow x=\frac{36}{19}\)
e)\(\left(x+4\right)\cdot\left(x^2-4x+16\right)-x\cdot\left(x-4\right)^2=8\cdot\left(x-3\right)\cdot\left(x+3\right)\)
\(\Leftrightarrow x^3+4^3-x^3+8x^2-16x-8x^2+72=0\)
\(\Leftrightarrow16x+136=0\)
\(\Rightarrow x=\frac{-136}{16}=\frac{-17}{2}\)
g)\(4\cdot\left(x-1\right)\cdot\left(x+2\right)-5\cdot\left(x+7\right)=\left(2x+3\right)^2-5x+3\)
\(\Leftrightarrow4x^2+4x-4x-8-5x-35-4x^2-12x-9+5x-3=0\)\(\Leftrightarrow-12x-55=0\)
\(\Rightarrow x=\frac{-55}{12}\)
h)\(\left(x-1\right)\cdot\left(x^2+x+1\right)+3\cdot\left(x-2\right)^2=x\cdot\left(x^2+3x-1\right)\)
\(\Leftrightarrow x^3-1+3x^2-12x+12-x^3-3x^2+x=0\)
\(\Leftrightarrow-11x+11=0\)
\(\Rightarrow x=1\)
i)\(\left(x+5\right)\cdot\left(x-5\right)-\left(x+3\right)\cdot\left(x^2-3x+9\right)=5-x\cdot\left(x^2-x-2\right)\)
\(\Leftrightarrow x^2-25-x^3-27-5+x^3-x^2-2x=0\)
\(\Leftrightarrow-2x-57=0\)
\(\Rightarrow x=\frac{-57}{2}\)
k)\(\left(x+2\right)^2-2\cdot\left(x+3\right)\cdot\left(x-4\right)=5-x\cdot\left(x-3\right)\)
\(\Leftrightarrow x^2+4x+4-2x^2+8x-6x+24-5+x^2-3x=0\)
\(\Leftrightarrow3x+23=0\)
\(\Rightarrow x=\frac{-23}{3}\)
l)\(\left(x+7\right)\cdot\left(x-7\right)-\left(x+2\right)^2=5\cdot\left(x-2\right)+\left(x-7\right)\)
\(\Leftrightarrow x^2-49-x^2-4x-4-5x+10-x+7=0\)
\(\Leftrightarrow-10x-36=0\)
\(\Rightarrow x=\frac{-36}{10}=\frac{-18}{5}\)
tick hết cho mình nha:))
