Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a)Ta có:
\(\left(x-3,5\right)^2+\left(y-\dfrac{1}{10}\right)^4\le0\)
\(\Rightarrow x-3,5=y-\dfrac{1}{10}=0\Leftrightarrow\left\{{}\begin{matrix}x=3,5\\y=\dfrac{1}{10}=0,1\end{matrix}\right.\)
b) Ta có:
\(\left(5x+1\right)^2=\dfrac{36}{49}\)
\(\Leftrightarrow\left[{}\begin{matrix}5x+1=\dfrac{6}{7}\\5x+1=\dfrac{-6}{7}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{35}\\x=\dfrac{-13}{35}\end{matrix}\right.\)
b: ta có: \(\left(5x+1\right)^2=\dfrac{36}{49}\)
\(\Leftrightarrow\left[{}\begin{matrix}5x+1=\dfrac{6}{7}\\5x+1=-\dfrac{6}{7}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}5x=\dfrac{-1}{7}\\5x=\dfrac{-13}{7}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{35}\\x=\dfrac{-13}{35}\end{matrix}\right.\)
Trả lời:
a, \(\left(5x+1\right)^2=36\)
\(\Leftrightarrow\orbr{\begin{cases}\left(5x+1\right)^2=6^2\\\left(5x+1\right)^2=\left(-6\right)^2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}5x+1=6\\5x+1=-6\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=-\frac{7}{5}\end{cases}}}\)
Vậy x = 1; x = - 7/5
b, \(\left(x-2\right)^3=2^6\)
\(\Leftrightarrow\left(x-2\right)^3=\left(2^2\right)^3\)
\(\Leftrightarrow\left(x-2\right)^3=4^3\)
\(\Leftrightarrow x-2=4\)
\(\Leftrightarrow x=6\)
Vậy x = 6
c, \(\left(8x-1\right)^{2x+1}=5^{2x+1}\)
\(\Leftrightarrow8x-1=5\)
\(\Leftrightarrow8x=6\)
\(\Leftrightarrow x=\frac{3}{4}\)
d, \(\left(x-3,5\right)^2+\left(y-1\right)^4\le0\)
Mà \(\left(x-3,5\right)^2\ge0\forall x;\left(y-1\right)^4\ge0\forall y\)
\(\Rightarrow\hept{\begin{cases}x-3,5=0\\y-1=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=3,5\\y=1\end{cases}}}\)
Vậy x = 3,5; y = 1
Căng, sự thật là nó rất căng
Nhg dù sao thì.....
1) \(A\left(x\right)=\left(x-4\right)^2-\left(2x+1\right)^2\)
Xét \(A\left(x\right)=0\)
\(\Rightarrow\left(x-4\right)^2-\left(2x+1\right)^2=0\)
\(\Rightarrow x^2-8x+16-4x^2-4x-1=0\)
\(\Rightarrow-3x^2-12x+15=0\)
\(\Rightarrow-3x^2+3x-15x+15=0\)
\(\Rightarrow-3x\left(x-1\right)-15\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(-3x-15\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\-3x-15=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-5\end{matrix}\right.\)
2)(Sửa đề nha, sai cmnr) \(B\left(x\right)=x^3+x^2-4x-4\)
Xét \(B\left(x\right)=0\)
\(\Rightarrow x^3+x^2-4x-4=0\)
\(\Rightarrow x^2\left(x+1\right)-4\left(x+1\right)=0\)
\(\Rightarrow\left(x^2-4\right)\left(x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x^2-4=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\pm2\\x=-1\end{matrix}\right.\)
Đó là những j mình biết 
1, \(\left(x-4\right)^2-\left(2x+1\right)^2=\left(x-4-2x-1\right)\left(x-4+2x+1\right)=-3\left(x+5\right)\left(x-1\right).\)
\(\orbr{\begin{cases}x+5=0\\x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-5\\x=1\end{cases}}}\)(mấy cái này áp dụng hàng đẳng thức lớp 8 mới hok)
2,\(x^3+x^2-4x-4=\left(x-2\right)\left(x^2+3x+2\right)=\left(x-2\right)\left(x+1\right)\left(x+2\right)\)
\(\orbr{\begin{cases}x=\mp2\\\end{cases}}x=-1\)
tương tụ lm tiếp nhe buồn ngủ quá rồi !
b: \(\left(x-\dfrac{2}{9}\right)^3=\left(\dfrac{y}{3}\right)^2=\left(\dfrac{2}{3}\right)^6\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-\dfrac{2}{9}\right)^3=\left(\dfrac{4}{9}\right)^3\\\left(\dfrac{y}{3}\right)^2=\left(\dfrac{8}{27}\right)^2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-\dfrac{2}{9}=\dfrac{4}{9}\\\dfrac{y}{3}=\dfrac{8}{27}\end{matrix}\right.\\\left\{{}\begin{matrix}x-\dfrac{2}{9}=\dfrac{4}{9}\\\dfrac{y}{3}=-\dfrac{8}{27}\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=\dfrac{2}{3}\\y=\dfrac{8}{9}\end{matrix}\right.\\\left\{{}\begin{matrix}x=\dfrac{2}{3}\\y=-\dfrac{8}{9}\end{matrix}\right.\end{matrix}\right.\)
c: =>8x-1=5
=>8x=6
hay x=3/4
(5x + 1)2 = 36/49
=> (5x + 1)2 = (6/7)2
=> \(\orbr{\begin{cases}5x+1=\frac{6}{7}\\5x+1=-\frac{6}{7}\end{cases}}\)
=> \(\orbr{\begin{cases}x=-\frac{1}{35}\\x=-\frac{13}{35}\end{cases}}\)
Làm từ phần b nha
b) \(\left(x-\frac{1}{9}\right)^3=\frac{2}{3}^6\)
\(\Rightarrow\left(x-\frac{2}{9}\right)^3=\left(\frac{1}{3}\right)^6\)
\(\Rightarrow\left(x-\frac{2}{3}\right)^3=\frac{1^6}{3^6}\)
\(\Rightarrow\left(x-\frac{2}{3}\right)^3=\frac{1}{3^6}\)
\(\Rightarrow\left(x-\frac{2}{3}\right)^3=\frac{1}{729}\)
\(\Rightarrow x-\frac{2}{9}=\frac{1}{9}\)
\(x=\frac{1}{9}+\frac{2}{9}\)
\(x=\frac{3}{9}=\frac{1}{3}\)
c) Sai đề rồi, xem lại đi
d) \(\left(x-3,5\right)^2+\left(y-\frac{1}{10}\right)^4< 0\)
\(\Rightarrow\frac{10000y^4-4000y^3+600y^3-40y+10000x^2+122501-70000x}{10000}< 0\)
=> Sai \(\forall y\inℝ\)