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a: \(\Leftrightarrow5x^2-20x-41=x^2-10x+25+4x^2+4x+1-x^2+2x+\left(x-1\right)^2\)
\(\Leftrightarrow5x^2-20x-41=4x^2-4x+26+x^2-2x+1\)
\(\Leftrightarrow5x^2-20x-41=5x^2-6x+27\)
=>-14x=68
hay x=-34/7
b: \(\Leftrightarrow x^2-25-x^3+6x^2-12x+8-7x^2+x^3+1=\left(x+3\right)^3-x^3-9x^2\)
\(\Leftrightarrow-12x-16=x^3+9x^2+27x+27-x^3-9x^2=27x+27\)
=>-39x=43
hay x=-43/39
1: \(\Leftrightarrow5x^2+4x-1-2x^2+12x-18=3x^2+5x-2-x^2-8x-16+x^2-x\)
\(\Leftrightarrow3x^2+16x-19=3x^2-4x-18\)
=>20x=1
hay x=1/20
2: \(\Leftrightarrow5x^2-20x-41=x^2-10x+25+4x^2+4x+1-\left(x^2-2x\right)+\left(x-1\right)^2\)
\(\Leftrightarrow5x^2-20x-41=4x^2-4x+26+x^2-2x+1\)
\(\Leftrightarrow-20x-41=-6x+27\)
=>-14x=68
hay x=-34/7
a) \(\left(4x-1\right)^2-\left(3x+2\right)\left(3x-2\right)=\left(7x-1\right)\left(x+2\right)+\left(2x+1\right)^2-\left(4x^2+7\right)\)(1)
\(\Leftrightarrow\left(16x^2-8x+1\right)-\left(9x^2-4\right)=\left(7x^2+14x-x-2\right)+\left(4x^2+4x+1\right)-\left(4x^2+7\right)\)
\(\Leftrightarrow16x^2-8x+1-9x^2+4=7x^2+13x-2+4x^2+4x+1-4x^2-7\)
\(\Leftrightarrow7x^2-8x+5=7x^2+17x-8\)
\(\Leftrightarrow7x^2-8x-7x^2-17x=-8-5\)
\(\Leftrightarrow-25x=-13\)
\(\Leftrightarrow x=\dfrac{13}{25}\)
Vậy tập nghiệm phương trình (1) là \(S=\left\{\dfrac{13}{25}\right\}\)
1.a) \(\Leftrightarrow\) 3x+10-2x =0
\(\Leftrightarrow\text{ 3x-2x=-10}\)
\(\Leftrightarrow x=-10\)
b) coi lại có thiếu ngoặc ko nhé
cứ nhân vào dấu ngoặc rồi làm như thường
1) \(\left(3x+4\right)\left(3x-4\right)-\left(2x+5\right)^2=\left(x-5\right)^2+\left(2x+1\right)^2-\left(x^2-2x\right)+\left(x-1\right)^2\)
\(\Leftrightarrow9x^2-16-4x^2-20x-25=x^2-10x+25+4x^2+4x+1-x^2+2x+x^2-2x+1\)
\(\Leftrightarrow9x^2-4x^2-x^2-4x^2+x^2-x^2-20x+10x-4x-2x+2x=25+1+1+16+25\)
\(\Leftrightarrow-14x=68\)
\(\Leftrightarrow x=-\dfrac{34}{7}\)
Vậy................
2) \(\left(x-5\right)\left(x+5\right)-\left(x-2\right)^3-7x^2+\left(x+1\right)\left(x^2-x+1\right)=\left(x+3\right)^3-\left(x^3+9x^2\right)\)
\(=x^2-25-x^3+6x^2-12x+8-7x^2+x^3+1=x^3+9x^2+27x+27-x^3-9x^2\)
\(\Leftrightarrow x^2+6x^2-7x^2-9x^2+9x^2-x^3+x^3-x^3+x^3-12x-27x=27-1-8+25\)
\(\Leftrightarrow-39x=43\)
\(\Leftrightarrow x=-\dfrac{43}{39}\)
Vậy................
1. ( 3x + 4 )( 3x - 4 ) - ( 2x + 5 )2 = ( x - 5 )2 + ( 2x + 1 )2 - ( x2 - 2x ) + ( x - 1 )2
⇔ 9x2 - 16 - 4x2 - 20x - 25 = x2 - 10x + 25 + 4x2 + 4x + 1 - x2 + 2x + x2 - 2x + 1
⇔ - 18x - 68 = 0
⇔ -2( 9x + 34 ) = 0
⇔ x = \(\dfrac{34}{9}\)
KL.....................
2) ( x - 5 )( x + 5 ) - ( x - 2 )3 - 7x2 + ( x + 1 )( x2 - x + 1 ) = ( x + 3 )3 - ( x3 + 9x2 )
⇔ x2 - 25 - x3 + 6x2 - 12x + 8 - 7x2 + x3 + 1 = x3 + 9x2 + 27x + 27 - x3 - 9x2
⇔ - 39x- 43 = 0
⇔ 39x + 43 = 0
⇔ x =\(-\dfrac{43}{39}\)
KL...................