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Câu b
5x-8=2x+7
<=> 3x=7+8=15
<=>x=5
Câu c:
<=>4x=3+5
<=>4x=8
<=>x=2
Câu d
<=>6=4x
<=> x=3/2
Câu e
<=> 2x+8-6x+15=3
<=>4x=20
<=>x=5
b)5x-8=2x+7
⇔3x=15
⇔ x=5
c)4x2+2x-5=4x2-2x+3
⇔ 4x=8
⇔ x=2
d)2x3-3x+6=2x3+x
⇔ 4x=6
⇔ \(x=\dfrac{3}{2}\)
e)2(x+4)-3(2x-5)=3
⇔ 2x+4-6x+15=3
⇔ -4x+19=3
⇔ 4x=16
⇔ x=4
\(\Delta'=4-\left(m-1\right)=5-m\)
để pt có nghiệm kép khi \(5-m=0\Leftrightarrow m=5\)
chọn B
Phương trình có nghiệm kép khi:
\(\Delta'=4-\left(m-1\right)=0\Leftrightarrow5-m=0\)
\(\Rightarrow m=5\)
Ex6
1 was
2 had been
3 found
4 had talked
5 had spoken
6 snowed
7 were
8 painted
9 had
10 had known
Ex7
2 had got
3 had hurt
4 were
5 were
6 was
7 wanted
8 ?
9 stopped
10 had eaten
\(pt\text{⇔}\left(x^2+3x+2\right)\left(x+5\right)-x^3-8x^2-27=0\text{⇔}x^3+5x^2+3x^2+15x+2x+10-x^3-8x^2-27=0\\ \text{⇔}17x=17\text{⇔}x=1\)
Vậy nghiệm của phương trình : \(S=\left\{1\right\}\)
Ta có: \(\left(x+1\right)\left(x+2\right)\left(x+5\right)-x^3-8x^2=27\)
\(\Leftrightarrow\left(x^2+3x+2\right)\left(x+5\right)-x^3-8x^2=27\)
\(\Leftrightarrow x^3+5x^2+3x^2+15x+2x+10-x^3-8x^2=27\)
\(\Leftrightarrow17x=17\)
hay x=1
h: \(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{9\cdot10}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=1-\dfrac{1}{10}=\dfrac{9}{10}\)
m: \(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)
\(=\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\)
\(=\dfrac{1}{2}-\dfrac{1}{8}=\dfrac{3}{8}\)
Câu 1:
$(x^2-1)(4x-x^2)=0$
$\Leftrightarrow (x-1)(x+1)x(4-x)=0$
$\Rightarrow x=\pm 1$ hoặc $x=0$ hoặc $x=4$
Vì $x\in\mathbb{N}$ nên $x\in\left\{0;4;1\right\}$
Đáp án B
Câu 2: C
Câu 3: D
Câu 4:
ĐKXĐ: $x^2-7x+12\neq 0$
$\Leftrightarrow (x-3)(x-4)\neq 0$
$\Leftrightarrow x-3\neq 0$ và $x-4\neq 0$
$\Leftrightarrow x\neq 3$ và $x\neq 4$
$\Leftrightarrow x\in\mathbb{R}\setminus\left\{3;4\right\}$
Đáp án D
Câu 5:
ĐKXĐ: \(\left\{\begin{matrix} 2-x\geq 0\\ x+7\geq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\leq 2\\ x\geq -7\end{matrix}\right.\Leftrightarrow x\in [-7;2]\)
Đáp án C.
Câu 6:
ĐKXĐ: \(\left\{\begin{matrix} 5-2x\geq 0\\ x-1\geq 0\\ (x-2)\sqrt{x-1}\neq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\leq \frac{5}{2}\\ x>1\\ x\ne 2\end{matrix}\right.\)