\(7x^2\)- 14x
tìm x
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Ta có $\sqrt{x^2-7x+19}-\sqrt{x^2-7x+15}=2$
$=>2M=(\sqrt{x^2-7x+19}-\sqrt{x^2-7x+15})(\sqrt{x^2-7x+19}+\sqrt{x^2-7x+15})$
$=>2M=\sqrt{x^2-7x+19}^2-\sqrt{x^2-7x+15}^2$
$=>2M=(x^2-7x+19)-(x^2-7x+15)=4$
$=>M=2$
\(2.M=\left(x^2-7x+19\right)-\left(x^2-7x+15\right)=4\Rightarrow M=2\)
Đặt \(\sqrt{x^2-7x+19}-\sqrt{x^2-7x+15}=B\) = B
Xét tích \(AB=\left(\sqrt{x^2-7x+19}-\sqrt{x^2-7x+15}\right)\left(\sqrt{x^2-7x+19}+\sqrt{x^2-7x+15}\right)\)
\(=x^2-7x+19-\left(x^2-7x+15\right)=x^2-7x+19-x^2+7x-15\)
\(=4\)
Mà \(B=2\Leftrightarrow A=2\)
Bài 12:
a) \(\left(\dfrac{1}{2}x+4\right)^2\)
\(=\left(\dfrac{1}{2}x\right)^2+2\cdot\dfrac{1}{2}x\cdot4+4^2\)
\(=\dfrac{1}{4}x^2+4x+16\)
b) \(\left(7x-5y\right)^2\)
\(=\left(7x\right)^2-2\cdot7x\cdot5y+\left(5y\right)^2\)
\(=49x^2-70xy+25y^2\)
c) \(\left(6x^2+y^2\right)\left(y^2-6x^2\right)\)
\(=\left(y^2+6x^2\right)\left(y^2-6x^2\right)\)
\(=y^4-36x^4\)
d) \(\left(x+2y\right)^2\)
\(=x^2+2\cdot x\cdot2y+\left(2y\right)^2\)
\(=x^2+4xy+4y^2\)
e) \(\left(x-3y\right)\left(x+3y\right)\)
\(=x^2-\left(3y\right)^2\)
\(=x^2-9y^2\)
f) \(\left(5-x\right)^2\)
\(=5^2-2\cdot5\cdot x+x^2\)
\(=25-10x+x^2\)
a) \(\left(3x-2\right)\left(3x-1\right)=\left(3x+1\right)^2\)
<=> \(9x^2-9x+2=9x^2+6x+1\)
<=> \(15x=1\) <=> \(x=\frac{1}{15}\)
b) \(\left(4x-1\right)\left(x+1\right)=\left(2x-3\right)^2\)
<=> \(4x^2+3x-1=4x^2-12x+9\)
<=> \(15x^2=10\) <=> \(x=\frac{2}{3}\)
c) \(\left(5x+1\right)^2=\left(7x-3\right)\left(7x+2\right)\) <=> \(25x^2+10x+1=49x^2-7x-6\)
<=> \(24x^2-17x-7=0\) <=> \(24x^2-24x+7x-7=0\)
<=> \(\left(24x+7\right)\left(x-1\right)=0\) <=> \(\orbr{\begin{cases}x=-\frac{7}{24}\\x=1\end{cases}}\)
d) (4 - 3x)(4 + 3x) = (9x - 3)(1 - x)
<=> 16 - 9x2 = 12x - 9x2 - 3
<=> 12x = 19
<=> x = 19/12
e) x(x + 1)(x + 2)(x + 3) = 24
<=> (x2 + 3x)(x2 + 3x + 2) = 24
<=> (x2 + 3x)2 + 2(x2 + 3x) - 24 = 0
<=> (x2 + 3x)2 + 6(x2 + 3x) - 4(x2 + 3x) - 24 = 0
<=> (x2 + 3x + 6)(x2 + 3x - 4) = 0
<=> \(\orbr{\begin{cases}x^2+3x+6=0\\x^2+3x-4=0\end{cases}}\)
<=> \(\orbr{\begin{cases}\left(x+\frac{3}{2}\right)^2+\frac{15}{4}=0\left(vn\right)\\\left(x+4\right)\left(x-1\right)=0\end{cases}}\)
<=> \(\orbr{\begin{cases}x=-4\\x=1\end{cases}}\)
g) (7x - 2)2 = (7x - 3)(7x + 2)
<=> 49x2 - 28x + 4 = 49x2 - 7x - 6
<=> 21x = 10 <=> x = 10/21
2|x-6|=|x-6|+7x+2-7x
2|x-6|=|x-6|+2
|x-6|=|x-6|+1
minh moi nghi den do thoi
2|x-6| + 7x -2 =|x-6| + 7x
=>2|x-6| -|x-6| - 2=7x-7x
=>|x-6|-2=0
=>|x-6|=2
=>x-6=2 hoặc x-6=-2
Phần sau tự giải
\(7x^2\left(x^2-5x+2\right)-5x\left(x^3-7x^2+3x\right)\)
\(=7x^4-35x^3+14x^2-5x^4+35x^3-15x^2\)
\(=2x^4-x^2\)
Thay: \(x=-\frac{1}{2}\) vào được
\(2.\left(-\frac{1}{2}\right)^4-\left(-\frac{1}{2}\right)^2\)
\(=2.\frac{1}{16}-\frac{1}{4}\)
\(=\frac{1}{8}-\frac{1}{4}=\frac{1}{8}-\frac{2}{8}=-\frac{1}{8}\)
P/s: Ko chắc
7x2 - 14x = 0
7x(x - 2) = 0
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x-2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}\)