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\(a,5^x+5^{x+2}=650\\ \Rightarrow a,5^x+5^x.25=650\\ \Rightarrow26.5^x=650\\ \Rightarrow5^x=25\\ \Rightarrow5^x=5^2\\ \Rightarrow x=2\)
\(b,3^{x.1}+5.3^{x.1}=162\\ \Rightarrow3^x+5.3^x=162\\ \Rightarrow6.3^x=162\\ \Rightarrow3^x=27\\ \Rightarrow3^x=3^3\\ \Rightarrow x=3\)
h(x) = x(x - 1) - 5x + 5 = x2 - x - 5x + 5 = x2 - 6x + 5
Ta có: x2 - 6x + 5 = 0
=> x2 - 5x - x + 5 = 0
=> x(x - 5) - (x - 5) = 0
=> (x - 5)(x - 1) = 0
=> x - 5 = 0 => x = 5
hoặc x - 1 = 0 => x = 1
Vậy x = 1, x = 5
a) A(x) = 0
=> 6x + 3 - (2x + 1)
=> 6x + 3 - 2x - 1 = 0
=> (6x - 2x) + (3 - 1) = 0
=> 4x + 2 = 0
=> 4x = -2
=> x = -2 : 4
=> x = -0,5
Vậy ...
b) B(x) = 0
=> (x2 + 5x - 5) - (5x - 5) = 0
=> x2 + 5x - 5 - 5x + 5 = 0
=> x2 + 5x - 5x = 0
=> x2 = 0
=> x = 0
Vậy ...
c) C(x) = x2 - 8x
=> x2 - 8x = 0
=> x2 = 8x
=> x = 8 ( Chia mỗi bên cho x)
Vậy ...
d) D(x) = x2 - 5x + 4
=> x2 - x - 4x + 4 = 0
=> x.(x - 1) - 4.(x - 1) = 0
=> (x - 4).(x - 1) = 0
=> \(\left[{}\begin{matrix}x-4=0\\x-1=0\end{matrix}\right.\) => \(\left[{}\begin{matrix}x=4\\x=1\end{matrix}\right.\)
Vậy x = 4; x = 1 là nghiệm của D(x)
Do x, y tỉ lệ thuận \(\Rightarrow\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}=\dfrac{4}{5}\div\dfrac{8}{15}=\dfrac{3}{2}\) \(\Rightarrow x_1=\dfrac{3}{2}y_1\)
\(y_1-x_1=\dfrac{-1}{4}\Rightarrow y_1-\dfrac{3}{2}y_1=\dfrac{-1}{4}\Rightarrow\dfrac{-1}{2}y_1=\dfrac{-1}{4}\)
\(\Rightarrow y_1=\dfrac{1}{2}\) \(\Rightarrow x_1=y_1-\dfrac{-1}{4}=\dfrac{3}{4}\)
5:
a: f(x)+h(x)=g(x)
=>h(x)=g(x)-f(x)
\(=-x^5-5x^3+4x+2-x^5+3x^3-2x+1=-2x^3+2x+3\)
b: g(x)-h(x)=f(x)
=>h(x)=g(x)-f(x)
=-2x^3+2x+3
a)\(5^x+5^{x+2}=650\Rightarrow5^x+5^2.5^x=650\Rightarrow5^x+25.5^x=650\Rightarrow26.5^x=650\)\(5^x=25\Rightarrow5^x=5^2\Rightarrow x=2\)
b) \(3^{x-1}+5.3^{x-1}=162\Rightarrow6.3^{x-1}=162\Rightarrow3^{x-1}=27=3^3\)x-1=3 nên x=4