Dịch giúp em bài 1 với ạ, em đang cần gấp T^T
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3) Ta có: \(\text{Δ}=\left[-2\left(m-1\right)\right]^2-4\cdot1\cdot\left(m^2-6\right)\)
\(=\left(2m-2\right)^2-4\left(m^2-6\right)\)
\(=4m^2-8m+4-4m^2+24\)
\(=-8m+28\)
Để phương trình có hai nghiệm phân biệt x1;x2 thì Δ>0
\(\Leftrightarrow-8m+28>0\)
\(\Leftrightarrow-8m>-28\)
hay \(m< \dfrac{7}{2}\)
Áp dụng hệ thức Vi-et, ta được:
\(\left\{{}\begin{matrix}x_1+x_2=\dfrac{2\left(m-1\right)}{1}=2m-2\\x_1x_2=m^2-6\end{matrix}\right.\)
Ta có: \(x_1^2+x_2^2=16\)
\(\Leftrightarrow\left(x_1+x_2\right)^2-2x_1x_2=16\)
\(\Leftrightarrow\left(2m-2\right)^2-2\left(m^2-6\right)-16=0\)
\(\Leftrightarrow4m^2-8m+4-2m^2+12-16=0\)
\(\Leftrightarrow2m^2-8m=0\)
\(\Leftrightarrow2m\left(m-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}m=0\left(nhận\right)\\m=4\left(loại\right)\end{matrix}\right.\)
1 Having slept
2 not being invited
3 Having had
4 having
5 talking
6 succeeded - launching
7 Having travelled
8 Have - considered - trying
9 Having seen - had - to go
10 Being invited
11 Being found
12 having
13 taken - being photographed
14 to fix
15 living
16 Having waited - to deliver - decided to cancel
17 Having photocopied
18 to have happen
19 to give
20 spoiling
a) \(\dfrac{A}{x-2}=\dfrac{x^2+3x+2}{x^2-4}\)
\(\Leftrightarrow\dfrac{A}{x-2}=\dfrac{\left(x+2\right)\left(x+1\right)}{\left(x-2\right)\left(x+2\right)}\)
\(\Leftrightarrow\dfrac{A}{x-2}=\dfrac{x+1}{x-2}\Leftrightarrow A=x+1\)
b) \(\dfrac{M}{x-1}=\dfrac{x^2+3x+2}{x+1}\)
\(\Leftrightarrow\dfrac{M}{x-1}=\dfrac{\left(x+1\right)\left(x+2\right)}{x+1}\)
\(\Leftrightarrow\dfrac{M}{x-1}=x+2\Leftrightarrow M=\left(x-1\right)\left(x+2\right)=x^2+x-2\)
Tìm số x nguyên dương biết:
Sao nữa ạ?