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X.(5X-4)-5(X^2+8)+10X=12
x5x-x4-5X^2-5.8+10X=12
X.(5X-4-5X)-40+10X=12
X.4-10.4+10X=12
4.X+10X-40=12
X.(4+10)=12+40
X.14=52
X=52:14
X=52PHAN14
\(\left(x^2-4\right)\left(x^2-10\right)=72\)
<=> \(x^4-14x^2+40-72=0\)
<=> \(x^4-14x^2-32=0\)
<=> \(\left(x^2-16\right)\left(x^2+2\right)=0\)
<=> \(\left[\begin{array}{nghiempt}x^2-16=0\\x^2+2=0\end{array}\right.\)=> x=\(\pm\)4
vậy tập nghiệm S={4;-4}
\(\left(x^2-4\right)\left(x^2-10\right)=72\)
\(\Leftrightarrow x^4-10x^2-4x^2+40=72\)
\(\Leftrightarrow x^4-14x^2+40-72=0\)
\(\Leftrightarrow x^4-14x^2-32=0\)
\(\Leftrightarrow x^4+2x^2-16x^2-32=0\)
\(\Leftrightarrow x^2\left(x^2+2\right)-16\left(x^2+2\right)=0\)
\(\Leftrightarrow\left(x^2+2\right)\left(x^2-16\right)=0\)
\(\Leftrightarrow\left(x^2+2\right)\left(x^2-4^2\right)=0\)
\(\Leftrightarrow\left(x^2+2\right)\left(x-4\right)\left(x+4\right)=0\left(1\right)\)
\(Có:x^2\ge0\)\(\text{ với mọi x}\)
\(\Rightarrow x^2+2\ge0+2=2\ne0\text{ với mọi x}\)
\(\left(1\right)\Leftrightarrow\left[\begin{array}{nghiempt}x-4=0\\x+4=0\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=4\\x=-4\end{array}\right.\)
\(\text{Vậy }x=\pm4\)
(x2-4)(x2-10)=72
=>x4-14x2+40=72
=>x4-14x2-32=0
=>(x-4)(x3+4x2+2x+8)=0
=>(x-4)(x+4)(x2+2)=0
=> (x-4) = 0 hoặc (x+4)=0 hoặc (x2+2)=0
=> x = 4 hoặc x=-4
\(x^4-2x^2+8=x^4+2x^2-4x^2+8=\left(x^2-4\right)\left(x^2+2\right)=\left(x-2\right)\left(x+2\right)\left(x^2+2\right)\)\(\left(x^4-2x^2-8\right):\left(x-2\right)=\left(x+2\right)\left(x^2+2\right)=0\)
\(\Rightarrow x=-2\)
a)\(\Leftrightarrow\left(9x^2-30x+25\right)-\left(9x^2+6x+1\right)\)
\(\Leftrightarrow9x^2-30x+25-9x^2-6x-1=8\)
\(\Leftrightarrow9x^2-30x-9x^2-6x=8-25+1\)
\(\Leftrightarrow-36x=-16\)
\(\Leftrightarrow x=\frac{4}{9}\)
Vậy \(x=\frac{4}{9}\)
b)\(\Leftrightarrow16x^2-6x-\left(16x^2-24x+9\right)=27\)
\(\Leftrightarrow16x^2-6x-16x^2+24x-9=27\)
\(\Leftrightarrow16x^2-6x-16x^2+24x=27+9\)
\(\Leftrightarrow18x=36\)
\(\Leftrightarrow x=2\)
Vậy \(x=2\)
Chúc bạn học tốt.
Ta có : 810x = 327x-5
=> 23.10x = 25(7x-5)
=> 3.10x = 5(7x-5)
=> 30x = 35x-25
=>30x-35x= -25
=>-5x = -25
=> x=5