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Đặt pt là (1)
Ta có :
(1) <=> \(\left[\left(x-3\right)\left(x-10\right)\right]\left[\left(x-5\right)\left(x-6\right)\right]-24x^2=0\)
\(\Leftrightarrow\left(x^2-13x+30\right)\left(x^2-11x+30\right)-24x^2=0\)
Đặt \(x^2-12x+30=t\) (*)
Phương trình trở thành \(\left(t-x\right)\left(t+x\right)-24x^2=0\)
\(\Leftrightarrow t^2-x^2-24x^2=0\)
\(\Leftrightarrow t^2-25x^2=0\)
\(\Leftrightarrow\left(t-5x\right)\left(t+5x\right)=0\)
Thay (*) vào ta có :
\(\left(x^2-17x+30\right)\left(x^2+7x+30\right)=0\)
Để ý thấy \(x^2-7x+30\ne0\)
\(\Rightarrow x^2-17x+30=0\)
\(\Leftrightarrow x^2-15x-2x+30=0\)
\(\Leftrightarrow x\left(x-15\right)-2\left(x-15\right)=0\)
\(\Leftrightarrow\left(x-15\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=15\end{matrix}\right.\)
Vậy S={1 ; 15 }
cảm ơn bạn nhìu
a)
\((x-3)(x-5)(x-6)(x-10)=24x^2\)
\(\Leftrightarrow [(x-3)(x-10)][(x-5)(x-6)]=24x^2\)
\(\Leftrightarrow (x^2-13x+30)(x^2-11x+30)=24x^2\)
Đặt \(x^2-11x+30=a\). PT trở thành:
\((a-2x)a=24x^2\)
\(\Leftrightarrow a^2-2ax-24x^2=0\)
\(\Leftrightarrow a^2-6ax+4ax-24x^2=0\)
\(\Leftrightarrow a(a-6x)+4x(a-6x)=0\)
\(\Leftrightarrow (a+4x)(a-6x)=0\)
\(\Rightarrow \left[\begin{matrix} a+4x=0\\ a-6x=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} x^2-7x+30=0\\ x^2-17x+30=0\end{matrix}\right.\)
\(\Rightarrow \left[\begin{matrix} (x-3,5)^2+17,75=0(\text{vô lý})\\ (x-15)(x-2)=0\end{matrix}\right.\)
\(\Rightarrow x=15\) hoặc $x=2$
b)
Đặt \(x-7=a\). PT trở thành:
\((a+1)^4+(a-1)^4=272\)
\(\Leftrightarrow a^4+4a^3+6a^2+4a+1+a^4-4a^3+6a^2-4a+1=272\)
\(\Leftrightarrow 2a^4+12a^2+2=272\)
\(\Leftrightarrow a^4+6a^2-135=0\)
\(\Leftrightarrow (a^2+3)^2-144=0\Leftrightarrow (a^2+3)^2-12^2=0\)
\(\Leftrightarrow (a^2+15)(a^2-9)=0\)
\(\Rightarrow a^2-9=0\Rightarrow a=\pm 3\)
\(\Rightarrow x=a+7=\left[\begin{matrix} 4\\ 10\end{matrix}\right.\)
(x-3)(x-5)(x-6)(x-10)-24x2
=(x-3)(x-10)(x-5)(x-6)-24x2
=(x2-13x+30)(x2-11x+30)-24x2
Đặt x2-12x+30=k
Khi đó ta có:
(k-x)(k+x)-24x2=k2-x2-24x2=k2-25x2
=(k-5x)(k+5x)
=(x2-12x+30-5x)(x2-12x+30+5x)
=(x2-17x+30)(x2-7x+30)
=(x2-2x-15x+30)(x2-7x+30)
=(x-2)(x-15)(x2-7x+30)
Ta có : |x - 2| + |x - 3| + |x - 4| + |x - 5| + |x - 6| -x + 7 = 0
=> |x - 2| + |x - 3| + |x - 4| + |x - 5| + |x - 6| = x - 7
ĐK \(x-7\ge0\Rightarrow x\ge7\)
Khi đó ta có x - 2 > 0 ; x - 3 > 0 ; ... x - 6 > 0
=> |x - 2| + |x - 3| + |x - 4| + |x - 5| + |x - 6| = x - 7
<=> x - 2 + x - 3 + x - 4 + x - 5 + x - 6 = x - 7
=> 5x - 20 = x - 7
=> 4x = 13
=> x = 4,25 (loại)
Vậy x \(\in\varnothing\)
\(\left(x-3\right)-\frac{\left(x-3\right)\left(2x-5\right)}{6}=\frac{\left(x-3\right)\left(3-x\right)}{4}\)
\(\Leftrightarrow\frac{12\left(x-3\right)}{12}-\frac{2\left(x-3\right)\left(2x-5\right)}{12}=\frac{3\left(x-3\right)\left(3-x\right)}{12}\)
\(\Leftrightarrow12\left(x-3\right)-2\left(x-3\right)\left(2x-5\right)=3\left(x-3\right)\left(3-x\right)\)
\(\Leftrightarrow12\left(x-3\right)-2\left(x-3\right)\left(2x-5\right)-3\left(x-3\right)\left(3-x\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(13-x\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}x-3=0\\13-x=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=3\\x=13\end{cases}}}\)
Vậy tập nghiệm của phương trình trên là:\(S=\left\{3;13\right\}\)
#hoktot<3#
\(\left(x-3\right)-\frac{\left(x-3\right)\left(2x-5\right)}{6}=\frac{\left(x-3\right)\left(3-x\right)}{4}\)
\(\frac{12\left(x-3\right)}{12}-\frac{\left(x-3\right)\left(2x-5\right)2}{12}=\frac{\left(x-3\right)\left(3-x\right)3}{12}\)
Khử mẫu : \(12\left(x-3\right)-\left(x-3\right)\left(2x-5\right)2=\left(x-3\right)\left(3-x\right)3\)
\(34x-66-4x^2=18x-3x^2-27\)
\(34x-66-4x^2-18x+3x^2+27=0\)
\(16x-39-x^2=0\)
Phân tích nốt nhé !
\(\left(x-2\right)^2+\left|x-5\right|-x^2-14=0.\)
\(\left(x^2-4x+4\right)+\left|x-5\right|-x^2-14=0.\)
\(x\text{}\text{}\text{}^2-4x+4+\left|x-5\right|-x^2-14=0.\)
\(x\text{}\text{}\text{}^2-x^2-4x+4-14+\left|x-5\right|=0.\)
\(-4x-10+\left|x-5\right|=0\)
.. đến đây xét tiếp để ra kq ạ -,-
\(\left(x-5\right)\left(x-1\right)=2x\left(x-1\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x-5-2x\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=-5\end{cases}}\)
Vậy............
\(5\left(x+3\right)\left(x-2\right)-3\left(x+5\right)\left(x+2\right)=0\)
\(\Leftrightarrow5\left(x^2+x-6\right)-3\left(x^2+7x+10\right)=0\)
\(\Leftrightarrow2x^2-16x-60=0\)
\(\Leftrightarrow x^2-8x-30=0\)
làm tiếp nhé!!!!!
\(\left(x-3\right)\left(x-5\right)\left(x-6\right)\left(x-10\right)=24x^2\) (1)
\(\Leftrightarrow\left(x^2-5x-3x+15\right)\left(x-6\right)\left(x-10\right)=24x^2\)
\(\Leftrightarrow\left(x^2-8x+15\right)\left(x-6\right)\left(x-10\right)=24x^2\)
\(\Leftrightarrow\left(x^3-6x^2-8x^2+48x+15x-90\right)\left(x-10\right)=24x^2\)
\(\Leftrightarrow\left(x^3-14x^2+63x-90\right)\left(x-10\right)=24x^2\)
\(\Leftrightarrow x^4-10x^3-14x^3+140x^2+63x^2-630x-90x+900=24x^2\)
\(\Leftrightarrow x^4-2x^3-22x^3+44x^2+135x^2-270x-450x+900=0\)
\(\Leftrightarrow x^3\left(x-2\right)-22x^2\left(x-2\right)+135x\left(x-2\right)-450\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^3-22x^2+135x-450\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^3-15x^2-7x^2+105x+30x-450\right)=0\)
\(\Leftrightarrow\left(x-2\right)\cdot\left[x^2\cdot\left(x-15\right)-7x\left(x-15\right)+30\left(x-15\right)\right]=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-15\right)\left(x^2-7x+30\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x-15=0\\x^2-7x+30=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=15\\x\notin R\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=15\end{matrix}\right.\)
Vậy tập nghiệm phương trình (1) là \(S=\left\{2;15\right\}\)
PT\(\Leftrightarrow\)\(\left[\left(x-3\right)\left(x-10\right)\right]\left[\left(x-5\right)\left(x-6\right)\right]=24x^2\)
\(\Leftrightarrow\)\(\left(x^2-13x+30\right)\left(x^2-11x+30\right)=24x^2\)
Nhận thấy x=0 không là nghiệm của PT. Chia cả hai vế của phương trình cho \(x^2\) ta được:
PT\(\Leftrightarrow\)\(\left(x-13+\dfrac{30}{x}\right)\left(x-11+\dfrac{30}{x}\right)=24\)
Đặt \(x+\dfrac{30}{x}=t\) (1)
PT\(\Leftrightarrow\)\(\left(t-13\right)\left(t-11\right)=24\)
Tìm được \(\left[{}\begin{matrix}t=17\\t=7\end{matrix}\right.\)
Thay vào (1):\(\left[{}\begin{matrix}x^2-17x+30=0\\x^2-7x+30=0\end{matrix}\right.\)
Tìm được \(\left[{}\begin{matrix}x=15\\x=2\end{matrix}\right.\)