a) \(\left(2x+1\right)^2-4\left(x+2\right)^2=9\\ \Rightarrow\left[2x+1-2\left(x+2\right)\right]\left[2x+1+2\left(x+2\right)\right]=9\\ \Rightarrow\left(2x+1-2x-4\right)\left(2x+1+2x+4\right)=9\\ \Rightarrow-3\left(4x+5\right)=9\\ \Rightarrow4x+5=-3\\ \Rightarrow4x=-8\\ \Rightarrow x=-2\)
\(b) (x+3)^2-(x-4)(x+8)=1 <=>x^2+6x=9-(x^2+8x-4x-32)=0 \)
\(.<=> X^2+6x+9-x^2-8x+4x+32-1=0\)
\(<=>2x=-40<=>x=-20\)
=> ptrình có tập nghiêm S={-20}
c) 3(x + 2)^2 + (2x - 1)^2 - 7(x + 3)(x - 3) = 36
\(<=>3(x^2+4x+4)+(4x^2-4x+1)-7(x^2-9)=36\)
\(<=>3x^2+12x+12+4x^2-4x+1-7x^2+49=0\)
\(<=>8x=-62<=>x=7,75\)
=> ptrình có tập nghiệm S={7,75}
d)d)(x - 3)(x^2 + 3x + 9) + x(x + 2)(2 - x) = 1
\(<=> x^3+3x^2+9x-3x^2-9x-27-x(x^2-4)=1\)
\(<=>x^3+3x^2+9x-3x^2-9x-27-x^3+4x-1=0\)
\(<=> 4x=28<=> x=7\)
=> ptrình có tập nghiệm S={7}
b)\(\Leftrightarrow\)\(x^2+6x+9-x^2-4x+32-1=0\)
\(\Leftrightarrow\)\(2x+40=0\)
\(\Leftrightarrow\)\(x=-20\)
c)\(\Leftrightarrow\)\(3(x^2+4x+4)+(4x^2-4x+1)-7(x^2-9)-36=0\)
\(\Leftrightarrow\)\(3x^2+12x+12+4x^2-4x+1-7x^2+63-36=0\)
\(\Leftrightarrow\)\(8x+40=0\)
\(\Leftrightarrow\)\(x=-5\)
d)\(\Leftrightarrow\)\(x^3+3x^2+9x-3x^2-9x-27+2x^2-3x^3+4x-2x^2-1=0\)
\(\Leftrightarrow\)\(4x-28=0\)
\(\Leftrightarrow\)\(x=7\)
