Bài1:
\(a,\left(2x+3\right)^2-\left(2x+1\right)\left(2x-1\right)=22\\ \Leftrightarrow\left(2x+3\right)^2-4x^2+1=22\\ \Leftrightarrow\left(2x+3-2x\right)\left(2x+3+2x\right)=21\\ \Leftrightarrow3\left(4x+3\right)=21\\ \Leftrightarrow4x+3=7\\ \Leftrightarrow4x=4\\ \Leftrightarrow x=1\\ Vậy....\\ b,\left(2x-1\right)^3-4x^2\left(2x-3\right)=5\\ \Leftrightarrow8x^3-12x^2+6x-1-8x^3+12x^2=5\\ \Leftrightarrow6x=6\\ \Leftrightarrow x=1\\ Vậy...\)
Các câu sau cũng như thế
Bài2:
\(A=x^2+20x+9\\ =\left(x^2+20x+100\right)-91\\ =\left(x+10\right)^2-91\)
Với mọi x thì \(\left(x+10\right)^2\ge0\\ \Rightarrow\left(x+10\right)^2-91\ge-91\)
Hay \(A\ge-91\)
Để A=-91 thì
\(\left(x+10\right)^2=0\\ \Leftrightarrow x+10=0\\ \Leftrightarrow x=-10\)
Vậy...
\(B=4x^2+5x+7\\ =\left(4x^2+5x+\dfrac{25}{16}\right)+5,4375\\ =\left(2x+\dfrac{5}{4}\right)^2+5,4375\)
Với mọi x;y thì \(\left(2x+\dfrac{5}{4}\right)^2+5,4375\ge5,4375\)
Hay \(A\ge5,4375\)
Để \(A=5,4375\) thì \(\left(2x+\dfrac{5}{4}\right)^2=0\\ \Leftrightarrow2x+\dfrac{5}{4}=0\\ \Leftrightarrow x=\dfrac{-5}{8}\)
Vậy....
