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...................
