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Ta có: \(f\left(1\right)=a+b+c=\left(a+c\right)+b=2^{2006}+2^{2007}\)
\(f\left(-1\right)=a-b+c=\left(a+c\right)-b=2^{2006}-2^{2007}\)
\(A=f\left(1\right)+f\left(-1\right)=\left(2^{2006}+2^{2007}\right)+\left(2^{2006}-2^{2007}\right)=2.2^{2006}=2^{2007}\)
\(B=f\left(1\right)-f\left(-1\right)=\left(2^{2006}+2^{2007}\right)-\left(2^{2006}-2^{2007}\right)=2.2^{2007}=2^{2008}\)
\(f\left(-1\right)=-a+b-c+d=2\)
\(f\left(0\right)=d=1\)
\(f\left(\frac{1}{2}\right)=\frac{1}{8}a+\frac{1}{4}b+\frac{1}{2}c+d=3\)
\(f\left(1\right)=a+b+c+d=7\)
Suy ra \(\hept{\begin{cases}-a+b-c=1\\\frac{1}{8}a+\frac{1}{4}b+\frac{1}{2}c=2\\a+b+c=6\end{cases}}\Leftrightarrow\hept{\begin{cases}2b=7\\\frac{1}{8}a+\frac{1}{4}b+\frac{1}{2}c=2\\a+b+c=6\end{cases}}\Leftrightarrow\hept{\begin{cases}a=\frac{1}{3}\\b=\frac{7}{2}\\c=\frac{13}{6}\end{cases}}\)
4. (3/4-81)(3^2/5-81)(3^3/6-81)....(3^6/9-81).....(3^2011/2014-81)
mà 3^6/9-81=0 => (3/4-81)(3^2/5-81)....(3^2011/2014-81)=0
\(f\left(-1\right)=a\left(-1\right)^2+b.\left(-1\right)+c\)
\(=a-b+c\)
\(f\left(2\right)=a.2^2+b.2+c\)
\(=4a+2b+c\)
\(\Rightarrow f\left(2\right)-2.f\left(-1\right)=\left(4a+2b+c\right)-2\left(a-b+c\right)\)
\(=2a+4b-c=0\)
\(\Rightarrow f\left(2\right)=2.f\left(-1\right)\)
\(\Rightarrow f\left(2\right)\)và \(2.f\left(-1\right)\)cùng dấu
\(\Rightarrow f\left(2\right)\)và \(f\left(-1\right)\)cùng dấu
\(\Rightarrow f\left(2\right).f\left(-1\right)\ge0\)(đpcm)
Ta có :\(f\left(-1\right)=a.\left(-1\right)^2+b.\left(-1\right)+c=a-b+c\)
\(f\left(2\right)=a.2^2+b.2+c=4a+2b+c\)
\(\implies\) \(f\left(2\right)-2f\left(-1\right)=\left(4a+2b+c\right)-2.\left(a-b+c\right)\)
\(\implies\) \(f\left(2\right)=2.f\left(-1\right)\)
\(\implies\) \(f\left(-1\right).f\left(2\right)=f\left(-1\right).2f\left(-1\right)=f\left(-1\right)^2.2\) \(\geq\) \(0\)
\(\implies\) \(f\left(-1\right).f\left(2\right)\) \(\geq\) \(0\) \(\left(đpcm\right)\)
Đồ thị hàm số đi qua O (0; 0)
Cho x = 2 ⇒ y = 1,5. 2 = 3
Ta có: A(2; 3)
Vẽ đường thẳng OA ta có đồ thị hàm số.
a) f(1) = 1,5. 1 = 1,5
f(-1) = 1,5. (-1) = -1,5
f(-2) = 1,5. (-2) = -3
f(2) = 1,5. 2 = 3
f(0) =0
b)\(y=-1\Rightarrow x=\dfrac{-1}{1,5}=-\dfrac{2}{3}\)
\(y=0\Rightarrow x=\dfrac{0}{1,5}=0\)
\(y=4,5\Rightarrow x=\dfrac{4,5}{1,5}=3\)
c) y > 0 ⇒1,5x > 0 ⇒x > 0
y < 0 ⇒ 1,5x < 0 ⇒ x < 0
Đồ thị hàm số đi qua O (0; 0)
Cho x = 2 ⇒⇒ y = 1,5. 2 = 3
Ta có: A(2; 3)
Vẽ đường thẳng OA ta có đồ thị hàm số.
a) f(1) = 1,5. 1 = 1,5
f(-1) = 1,5. (-1) = -1,5
f(-2) = 1,5. (-2) = -3
f(2) = 1,5. 2 = 3
f(0) = 0
b)y=−1⇒x=\(\dfrac{-1}{1,5}=-\dfrac{2}{3}\)
b)y=0⇒x==\(\dfrac{0}{1,5}=0\)
y=4,5⇒x=\(\dfrac{4,5}{1,5}=3\)
c) y > 0 ⇒1,5x > 0 ⇒x > 0
y < 0 ⇒ 1,5x < 0 ⇒ x < 0
\(f\left(1\right)=a\cdot1^2+b\cdot1+c=a+c+b=2^{2006}+2^{2006}=2\cdot2^{2006}=2^{2007}\\ f\left(-1\right)=a\cdot\left(-1\right)^2+b\cdot\left(-1\right)+c=a+c-b=2^{2006}-2^{2006}=0\\ A=f\left(-1\right)+f\left(1\right)=0+2^{2007}=2^{2007}\\ B=f\left(1\right)-f\left(-1\right)=2^{2007}-0=2^{2007}\)
Câu b xem lại đề