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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: \(\Leftrightarrow\left(3x+2\right)\left(5-x\right)=-9x^2+4\)
\(\Leftrightarrow\left(3x+2\right)\left(5-x\right)+\left(3x+2\right)\left(3x-2\right)=0\)
\(\Leftrightarrow\left(3x+2\right)\left(2x+3\right)=0\)
=>x=-2/3 hoặc x=-3/2
b: \(\Leftrightarrow4x\left(x+5\right)+x^2-25=0\)
\(\Leftrightarrow\left(x+5\right)\left(5x-5\right)=0\)
=>x=-5 hoặc x=1
c: \(\Leftrightarrow3x\left(x-1\right)=\left(x-1\right)^2\)
\(\Leftrightarrow\left(x-1\right)\left(2x+1\right)=0\)
=>x=1 hoặc x=-1/2
1, x3+ 6x2+11x+6
= x3 + 2x2 + 4x2 + 8x + 3x + 6
= x2(x + 2) + 4x(x + 2) + 3(x + 2)
= (x + 2)(x2 + 4x + 3)
2, x4+3x3-7x2-27x-18
= x4 + 3x3 - 9x2 + 2x2 - 27x -18
= (x4 - 9x2) + (3x3 - 27x) + (2x2 - 18)
= x2(x2 - 9) + 3x(x2 - 9) + 2(x2 - 9)
= (x2 - 9)(x2 + 3x + 2)
= (x + 3)(x - 3)(x2 + 3x + 2)
3, x3-8x2+x+42
= x3 - 7x2 - x2 + 7x - 6x + 42
= (x3 - 7x2) - (x2 - 7x) - (6x - 42)
= x2(x - 7) - x(x - 7) - 6(x - 7)
= (x - 7)(x2 - x - 6)
4, x4+5x3-7x2-41x-30
= x4 + x3 + 4x3 - 4x2 - 11x2 - 11x - 30x - 30
= (x4 + x3) + (4x3 - 4x2) - (11x2 + 11x) - (30x + 30)
= x3(x + 1) + 4x2(x + 1) - 11x(x + 1) - 30(x + 1)
= (x3 + 4x2 - 11x - 30)(x + 1)
5, x5+x-1
= x5 - x4 + x3 + x4 - x3 + x2 - x2+ x -1
= x3(x2 - x + 1)+ x2(x2 - x + 1)- (x2 - x + 1)
= (x2 - x + 1)(x3 + x2 - 1)
6, x5-x4-1
= x5 - x3 - x2 - x4 + x2 + x + x3 - x - 1
= x2(x3 - x - 1) - x(x3 - x - 1) + (x3 - x - 1)
= (x2 - x + 1)(x3 - x - 1)
1, x 3+ 6x 2+11x+6
= x 3 + 2x 2 + 4x 2 + 8x + 3x + 6
= x 2 ﴾x + 2﴿ + 4x﴾x + 2﴿ + 3﴾x + 2﴿
= ﴾x + 2﴿﴾x 2 + 4x + 3﴿
2, x 4+3x 3‐7x 2‐27x‐18
= x 4 + 3x 3 ‐ 9x 2 + 2x 2 ‐ 27x ‐18
= ﴾x 4 ‐ 9x 2 ﴿ + ﴾3x 3 ‐ 27x﴿ + ﴾2x 2 ‐ 18﴿
= x 2 ﴾x 2 ‐ 9﴿ + 3x﴾x 2 ‐ 9﴿ + 2﴾x 2 ‐ 9﴿
= ﴾x 2 ‐ 9﴿﴾x 2 + 3x + 2﴿
=﴾x + 3﴿﴾x ‐ 3﴿﴾x 2 + 3x + 2﴿
3, x 3‐8x 2+x+42
= x 3 ‐ 7x 2 ‐ x 2 + 7x ‐ 6x + 42
= ﴾x 3 ‐ 7x 2 ﴿ ‐ ﴾x 2 ‐ 7x﴿ ‐ ﴾6x ‐ 42﴿
= x 2 ﴾x ‐ 7﴿ ‐ x﴾x ‐ 7﴿ ‐ 6﴾x ‐ 7﴿
= ﴾x ‐ 7﴿﴾x 2 ‐ x ‐ 6﴿
4, x 4+5x 3‐7x 2‐41x‐30
= x 4 + x 3 + 4x 3 ‐ 4x 2 ‐ 11x 2 ‐ 11x ‐ 30x ‐ 30
= ﴾x 4 + x 3 ﴿ + ﴾4x 3 ‐ 4x 2 ﴿ ‐ ﴾11x 2 + 11x﴿ ‐ ﴾30x + 30﴿
= x 3 ﴾x + 1﴿ + 4x 2 ﴾x + 1﴿ ‐ 11x﴾x + 1﴿ ‐ 30﴾x + 1﴿
= ﴾x 3 + 4x 2 ‐ 11x ‐ 30﴿﴾x + 1﴿
5, x 5+x‐1
= x 5 ‐ x 4 + x 3 + x 4 ‐ x 3 + x 2 ‐ x 2+ x ‐1
= x 3 ﴾x 2 ‐ x + 1﴿+ x 2 ﴾x 2 ‐ x + 1﴿‐ ﴾x 2 ‐ x + 1﴿
= ﴾x 2 ‐ x + 1﴿﴾x 3 + x 2 ‐ 1﴿ 6, x 5‐x 4‐1
= x 5 ‐ x 3 ‐ x 2 ‐ x 4 + x 2 + x + x 3 ‐ x ‐ 1
= x 2 ﴾x 3 ‐ x ‐ 1﴿ ‐ x﴾x 3 ‐ x ‐ 1﴿ + ﴾x 3 ‐ x ‐ 1﴿
= ﴾x 2 ‐ x + 1﴿﴾x 3 ‐ x ‐ 1﴿
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...................
\(\left(5\cdot\left(x^2-3x+1\right)+x\cdot\left(1-5x\right)\right)-\left(x-2\right)=0\)
\(7-15x=0\)
\(-15x=-7\)
\(x=\frac{7}{15}=0.467\)
\(b,\)câu b dài quá nên mik lười, vậy mik ghi kết quả thôi nhé
\(x=\frac{2}{19}=0.105\)
\(c,\)câu c cũng vậy mik ghi kết quả thôi nhé bn
\(x=-\frac{6}{11}=-0.545\)