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\(1,=-\left(y^2+12y+36\right)=-y^2-12y-36\)
\(2,=-\left(16-8y+y^2\right)=-16+8y-y^2\)
\(3,=-\left(\dfrac{4}{9}+\dfrac{4}{3}x+x^2\right)=-\dfrac{4}{9}-\dfrac{4}{3}x-x^2\)
\(4,=-\left(x^2-3x+\dfrac{9}{4}\right)=-x^2+3x-\dfrac{9}{4}\)
\(5,-\left(2+3y\right)^2=-\left(4+12y+9y^2\right)=-4-12y-9y^2\)
.... mấy ý còn lại bn tự lm nhé, tương tự thhooi
1) \(-\left(y+6\right)^2=-y^2-12y-36\)
2) \(-\left(4-y\right)^2=-y^2+8y-16\)
3) \(-\left(x+\dfrac{2}{3}\right)^2=-x^2-\dfrac{4}{3}x-\dfrac{4}{9}\)
4) \(-\left(x-\dfrac{3}{2}\right)^2=-x^2+3x-\dfrac{9}{4}\)
5) \(-\left(3y+2\right)^2=-9y^2-12y-4\)
6) \(-\left(2y-3\right)^2=-4y^2+12y-9\)
7) \(-\left(5x+2y\right)^2=-25x^2-20xy-4y^2\)
8) \(-\left(2x-\dfrac{3}{2}\right)^2=-4x^2+6x-\dfrac{9}{4}\)
- Ở câu a thì bạn chỉ cần quy đồng mẫu ở các vế cho bằng nhau, rồi bỏ mẫu. Bạn cứ thế mà thực hiện phép tính thôi.
- Còn câu b thì giải như vầy:
<=> \(\frac{x-23}{24}+\frac{x-23}{25}-\frac{x-23}{26}-\frac{x-23}{27}=0\)
<=>\(\left(x-23\right)\left(\frac{1}{24}+\frac{1}{25}+\frac{1}{26}+\frac{1}{27}\right)=0\)
Vì \(\left(\frac{1}{24}+\frac{1}{25}+\frac{1}{26}+\frac{1}{27}\right)\ne0\)
<=> \(x-23=0\)
<=>\(x=23\)
Vậy phương trình có tập nghiệm: \(S=\left\{23\right\}\)
\(\frac{x-19}{24}\)+ \(\frac{x-19}{25}\)= \(\frac{x-19}{26}\)+ \(\frac{x-19}{27}\)
<=> \(\frac{x-19}{24}\)+ \(\frac{x-19}{25}\)- \(\frac{x-19}{26}\)- \(\frac{x-19}{27}\)= 0
<=> \(\frac{x}{24}\)- \(\frac{19}{24}\)+ \(\frac{x}{25}\)- \(\frac{19}{25}\)- \(\frac{x}{26}\)+\(\frac{19}{26}\)- \(\frac{x}{27}\)+\(\frac{19}{27}\)= 0
<=> \(\left(\frac{x}{24}+\frac{x}{25}-\frac{x}{26}-\frac{x}{27}\right)+\left(-\frac{19}{24}-\frac{19}{25}+\frac{19}{26}-\frac{19}{27}\right)=0\)
<=> \(x\left(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27}\right)-19\left(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27}\right)=0\)
<=> \(x\left(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27}\right)\)= \(19\left(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27}\right)\)
<=> x = 19
\(\frac{x+24}{1996}+\frac{x+25}{1995}+\frac{x+26}{1994}+\frac{x+27}{1993}+\frac{x+2036}{4}=0\\ \Leftrightarrow\left(\frac{x+24}{1996}+1\right)+\left(\frac{x+25}{1995}+1\right)+\left(\frac{x+26}{1994}+1\right)+\left(\frac{x+27}{1993}+1\right)+\left(\frac{x+2036}{4}-4\right)=0\\ \Leftrightarrow\frac{x+2020}{1996}+\frac{x+2020}{1995}+\frac{x+2020}{1994}+\frac{x+2020}{1993}+\frac{x+2020}{4}=0\\ \Leftrightarrow\left(x+2020\right)\left(\frac{1}{1996}+\frac{1}{1995}+\frac{1}{1994}+\frac{1}{1993}+\frac{1}{4}\right)=0\\\Leftrightarrow x+2020=0\\\Leftrightarrow x=-2020\)
Vậy pt có tập nghiệm \(S=\left\{-2020\right\}\)
\(\Leftrightarrow\frac{x+24}{1996}+1+\frac{x+25}{1995}+1+\frac{x+26}{1994}+1+\frac{x+27}{1993}+1+\frac{x+2036}{4}-4=0\)
\(\Leftrightarrow\left(x+2020\right)\left(...\right)=0\Rightarrow x=-2020\)