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Bài 2 :
a, bạn tự vẽ
b, \(\left\{{}\begin{matrix}x^2-x-2=0\\y=x^2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1;x=2\\y=1;y=4\end{matrix}\right.\)
Vậy (d) cắt (P) tại A(-1;1) ; B(2;4)
Tổng 2 số: 30*2=60
Số thứ 1: 60/(4+1)*4=48
Số thứ 2: 60-48=12
Vậy St1=48, St2=12
Tổng 2 số là :
30 x 2 = 60
Ta có sơ đồ :
St1 :|___|___|___|___| tổng : 60
St2 :|___|
Tổng số phần bằng nhau là :
4 + 1 = 5 (phần)
St1 là :
60 : 5 x 4 = 48
St2 là :
60 - 48 = 12
Đ/S : st1 : 48
st2 : 12
a: \(A=\dfrac{x^2+2x+1-1}{2\left(x-1\right)\left(x+1\right)}\cdot\dfrac{2\left(x+1\right)}{x+2}\)
\(=\dfrac{x\left(x+2\right)}{2\left(x-1\right)}\cdot\dfrac{2}{x+2}=\dfrac{x}{x-1}\)
b: x(x-2)-(x-2)=0
=>(x-2)(x-1)=0
=>x=2(nhận) hoặc x=1(loại)
Khi x=2 thì A=2/(2-1)=2
`1)\sqrt{50}-3\sqrt{8}+\sqrt{32}=5\sqrt{2}-6\sqrt{2}+4\sqrt{2}=3\sqrt{2}`
`2)`
`a)\sqrt{x^2-4x+4}=1`
`<=>\sqrt(x-2)^2}=1`
`<=>|x-2|=1`
`<=>[(x-2=1),(x-2=-1):}<=>[(x=3),(x=1):}`
`b)\sqrt{x^2-3x}-\sqrt{x-3}=0` `ĐK: x >= 3`
`<=>\sqrt{x}\sqrt{x-3}-\sqrt{x-3}=0`
`<=>\sqrt{x-3}(\sqrt{x}-1)=0`
`<=>[(\sqrt{x-3}=0),(\sqrt{x}-1=0):}`
`<=>[(x-3=0),(\sqrt{x}=1):}<=>[(x=3(t//m)),(x=1(ko t//m)):}`
Theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=\dfrac{3}{2}\\x_1x_2=-\dfrac{7}{2}\end{matrix}\right.\)
\(A=x_1^2+x_2^2=\left(x_1+x_2\right)^2-2x_1x_2=\dfrac{37}{4}\)
\(B=x_1^3+x_2^3=\left(x_1+x_2\right)^3-3x_1x_2\left(x_1+x_2\right)=\dfrac{153}{8}\)
\(C=x_1^4+x_2^4=\left(x_1^2+x_2^2\right)^2-2\left(x_1x_2\right)^2=\dfrac{977}{16}\)
\(D=\left|x_1-x_2\right|=\sqrt{\left(x_1-x_2\right)^2}=\sqrt{\left(x_1+x_2\right)^2-4x_1x_2}=\dfrac{\sqrt{65}}{2}\)
\(E=\left(2x_1+x_2\right)\left(2x_2+x_1\right)=2\left(x_1^2+x_2^2\right)+5x_1x_2=1\)
`a,` Đthang đi qua `A(3, 12)`.
`-> x = 3, y = 12 in y`.
`<=> 12 = 9a.`
`<=> a = 12/9 = 4/3.`
`b,` Đthang đi qua `B(-2;3)`.
`=> x = -2, y = 3 in y`.
`<=> 3=4a`.
`<=> a = 3/4`.
`3x^2+10x+3=0`
Ptr có: `\Delta'=5^2-3.3=16 > 0`
`=>` Ptr có `2` nghiệm pb
`=>` Áp dụng Viét có: `{(x_1+x_2=[-b]/a=-10/3),(x_1 .x_2=c/a=1):}`
~~~~~~~~~~~~~
`A=x_1 ^2+x_2 ^2`
`A=(x_1+x_2)^2-2x_1 .x_2`
`A=(-10/3)^2-2.1=82/9`
_______________________________________________________
`B=x_1 ^3+x_2 ^3`
`B=(x_1+x_2)(x_1 ^2-x_1 .x_2+x_2 ^2)`
`B=(x_1+x_2)[(x_1+x_2)^2 -3x_1 .x_2]`
`B=(-10/3).[(-10/3)^2-3.1]=-730/27`
_______________________________________________________
`C=x_1 ^4+x_2 ^4`
`C=(x_1 ^2+x_2 ^2)^2 -2x_1 ^2 .x_2 ^2`
`C=[(x_1+x_2)^2-2x_1 .x_2]^2-2(x_1 .x_2)^2`
`C=[(-10/3)^2-2.1]^2-2. 1^2=6562/81`
_______________________________________________________
`D=|x_1-x_2|`
`D=\sqrt{(x_1-x_2)^2}`
`D=\sqrt{(x_1+x_2)^2-4x_1.x_2}`
`D=\sqrt{(-10/3)^2-4.1}=8/3`
_______________________________________________________
`E=(2x_1+x_2)(2x_2+x_1)`
`E=4x_1 .x_2+2x_1 ^2+2x_2 ^2+x_1 .x_2`
`E=5x_1 . x_2+2(x_1+x_2)^2-4x_1 .x_2`
`E=x_1 .x_2+2(x_1+x_2)^2`
`E=1+2(-10/3)^2=209/9`
\(I\in d:\left\{{}\begin{matrix}x=-1+2t\\y=2t\\z=-4+t\end{matrix}\right.\left(t\in Z\right)\)
\(\Rightarrow I\left(-1+2t;2t;-4+t\right)\) và \(M\left(4;5;1\right)\)
\(\Rightarrow\overrightarrow{IM}=\left(5-2t;5-2t;5-t\right)\)
\(\Rightarrow R^2=IM^2=\left(5-2t\right)^2+\left(5-2t\right)^2+\left(5-t\right)^2\)
\(d\left(I;\left(P\right)\right)=\dfrac{\left|2\cdot\left(-1+2t\right)+2\cdot2t-\left(-4+t\right)\right|}{\sqrt{2^2+2^2+\left(-1\right)^2}}=\dfrac{\left|7t+2\right|}{3}\)
\(\Rightarrow d^2\left(I;\left(P\right)\right)=\dfrac{\left(7t+2\right)^2}{9}\)
\(R^2=d^2\left(I;\left(P\right)\right)+r^2\)
\(\Rightarrow\left(5-2t\right)^2+\left(5-2t\right)^2+\left(5-t\right)^2=\dfrac{\left(7t+2\right)^2}{9}+25\)
\(\Leftrightarrow16t^2-239t+223=0\Leftrightarrow\left[{}\begin{matrix}t=1\\t=\dfrac{223}{16}\left(l\right)\end{matrix}\right.\)
\(\Rightarrow I\left(1;2;-3\right)\Rightarrow\left\{{}\begin{matrix}a=1\\b=2\\c=-3\end{matrix}\right.\)
Vậy \(a+b+c=0\)
Chọn B.