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( 5x + 1 )2 = 36/49
<=> ( 5x + 1 )2 = ( ±6/7 )2
<=> 5x + 1 = 6/7 hoặc 5x + 1 = -6/7
<=> x = -1/35 hoặc x = -13/35
\(\left(5x+1\right)^2=\frac{36}{49}\)
\(\Rightarrow\orbr{\begin{cases}5x+1=\frac{6}{7}\\5x+1=\frac{-6}{7}\end{cases}}\)\(\)
\(\Rightarrow\orbr{\begin{cases}5x=\frac{-1}{7}\\5x=\frac{-13}{7}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{-1}{35}\\x=\frac{-13}{35}\end{cases}}\)
a) \(5^x\cdot5^6=5^4\)
\(5^x=5^{4-6}\)
\(5^x=5^{-2}\)
=> x = -2
b) \(\left(5x+1\right)^2=\left(\pm\frac{6}{7}\right)^2\)
+) 5x + 1 = 6/7
5x = -1/7
x = -1/35
+) 5x + 1 = -6/7
5x = -13/7
x = -13/35
Vậy,.........
\(\left(5x+1\right)^2=\left(\frac{\pm6}{7}\right)^2\)
+) 5x + 1 = 6/7
5x = -1/7
x = -1/35
+) 5x + 1 = -6/7
5x = -13/7
x = -13/35
Vậy,.........
(5x+1)2 =\(\frac{36}{49}\)
(5x+1)2=\(\frac{6}{7}^2\)
=>(5x+1)=\(\frac{6}{7}\)
5x =\(\frac{6}{7}\)-1=\(\frac{-1}{7}\)
x = \(\frac{-1}{7}\) :5
x= \(\frac{-1}{35}\)
(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 \(\forall y\inℝ\)
\(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)
\(\left(x-7\right)^{x+1}.\left[1-\left(x-7\right)^{10}\right]=0\)
\(\Rightarrow\orbr{\begin{cases}\left(x-7\right)^{x+1}=0\\\left(x-7\right)^{10}=1\end{cases}\Rightarrow\orbr{\begin{cases}x=7\\x-7=\pm1\end{cases}}}\)
vậy x=7, x=8 hay x=6
\(\left(5x+1\right)^2=\frac{36}{49}\)
(+) TH 1: 5x + 1 = 6/7
5x = 6/7 - 1
5x = -1/7
x = -1/7 : 5
x = -1 /35
(+) TH2 : 5x + 1 = - 6/7
5x = -6/7 - 1
5x = -13/7
x =-13/7 : 5
x = -13/35