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A = (x - 1)(x + 3) - (x - 2)(5x - 4)
A = x2 + 2x - 3 - 5x2 + 14x - 8
A = -4x2 + 16x - 11
B = (3a - 2b)(9a2 + 6ab - 4b2)
B = 27a3 + 18a2b - 12ab2 - 18a2b - 12ab2 + 8b3
B = 27a3 -24ab2 + 8b3
C = (x - 1)(x + 1) - (2x - 3)(4 - 5x)
C = x2 - 1 - 8x + 10x + 12 - 15x
C = x2 - 13x + 11
a) \(A=5x\left(4x^2-2x+1\right)-2x\left(10x^2-5x-2\right)\)
\(A=20x^3-10x^2+5x-20x^3+10x^2+4x\)
\(A=9x\)
Thay x = 15 vào, ta có:
\(A=9.15=135\)
b) \(B=5x\left(x-4y\right)-4y\left(y-5x\right)\)
\(B=5x^2-20xy-4y^2+20xy\)
\(B=5x^2-4y\)
Thay \(x=-\frac{1}{5};y=-\frac{1}{2}\) vào, ta có:
\(B=5.\left(-\frac{1}{5}\right)^2-4.\left(-\frac{1}{2}\right)=\frac{11}{5}\)
c) \(C=6xy\left(xy-y^2\right)-8x^2\left(x-y^2\right)-5y^2\left(x^2-xy\right)\)
\(C=6x^2y^2-6xy^3-8x^3+8x^2y^2-5x^2y^2+5xy^3\)
\(C=9x^2y^2-xy^3-8x^3\)
Thay \(x=\frac{1}{2};y=2\) vào, ta có:
\(C=9.\left(\frac{1}{2}\right)^2.2^2-\frac{1}{2}.2^3-8.\left(\frac{1}{2}\right)^3=4\)
d) \(D=\left(3x+5\right)\left(2x-1\right)+\left(4x-1\right)\left(3x+2\right)\)
\(D=6x^2-3x+10x-5+12x^2+8x-3x-2\)
\(D=18x^2+12x-7\)
Ta có: \(\left|2\right|=\orbr{\begin{cases}x=-2\\x=2\end{cases}}\)
+) Với x = -2
\(D=18.\left(-2\right)^2+12.\left(-2\right)-7=41\)
+) Với x = 2
\(D=18.2^2+12.2-7=89\)
a, Ta có : \(-x^2+2x-1-3\)
\(=-\left(x-1\right)^2-3\)
Ta thấy : \(\left(x-1\right)^2\ge0\forall x\)
=> \(-\left(x-1\right)^2-3\le-3\forall x\)
Vậy Max = -3 <=> x = 1 .
b, Ta có : \(-x^2-4x-4+4\)
\(=-\left(x+2\right)^2+4\)
Ta thấy : \(\left(x+2\right)^2\ge0\forall x\)
=> \(-\left(x+2\right)^2+4\le4\forall x\)
Vậy Max = 4 <=> x = -2 .
c, Ta có : \(-9x^2+24x-16-2\)
\(=-9\left(x^2-\frac{2.4x}{3}+\frac{16}{9}\right)-2\)
\(=-9\left(x-\frac{4}{3}\right)^2-2\)
Ta thấy : \(\left(x-\frac{4}{3}\right)^2\ge0\forall x\)
=> \(-9\left(x-\frac{4}{3}\right)^2-2\le-2\forall x\)
Vậy Max = -2 <=> x = \(\frac{4}{3}\) .
d, Ta có : \(-x^2+4x-4+3\)
\(=-\left(x-2\right)^2+3\)
Ta thấy : \(\left(x-2\right)^2\ge0\forall x\)
=> \(-\left(x-2\right)^2+3\le3\forall x\)
Vậy Max = 3 <=> x = 2 .
e, Ta có : \(-x^2+2x-1-4y^2-4y-1+7\)
\(=-\left(x-1\right)^2-4\left(y^2+y+\frac{1}{4}\right)+7\)
\(=-\left(x-1\right)^2-4\left(y+\frac{1}{2}\right)^2+7\)
Ta thấy : \(\left\{{}\begin{matrix}\left(x-1\right)^2\\\left(y+\frac{1}{2}\right)^2\end{matrix}\right.\) \(\ge0\forall xy\)
=> \(\left\{{}\begin{matrix}-\left(x-1\right)^2\\-4\left(y+\frac{1}{2}\right)^2\end{matrix}\right.\) \(\le0\forall xy\)
=> \(=-\left(x-1\right)^2-4\left(y+\frac{1}{2}\right)^2\le0\forall xy\)
=> \(=-\left(x-1\right)^2-4\left(y+\frac{1}{2}\right)^2+7\le7\forall xy\)
Vậy Max = 7 <=> \(\left\{{}\begin{matrix}x=1\\y=-\frac{1}{2}\end{matrix}\right.\)
a/ \(A=20x^3-10x^2+5x-20x^3+10x^2+4x=9x\)
Thay x = 15 vào bt A ta có
A = 9 . 15 = 135
b/ \(B=5x^2-20xy-4y^2+2xy=5x^2-4y^2\)
Thay x = -1/5 ; y = - 1/2 vào bt B ta có
\(B=5.\dfrac{1}{25}-4.\dfrac{1}{4}=\dfrac{1}{5}-1=-\dfrac{4}{5}\)
c/ \(C=6x^2y^2-6xy^3-8x^3+8x^2y^2-5x^2y^2+5xy^3\)
\(=9x^2y^2-xy^3-8x^3\)
Thay x = 1/2 ; y = 2 vào bt C ta có
\(C=9.4.\dfrac{1}{4}-\dfrac{1}{2}.8-8.\dfrac{1}{8}=9-4-1=4\)
d/ \(D=6x^2+10x-3x-5+6x^2-3x+8x-2\)
\(=12x^2+12x-3\)
\(\left|x\right|=2\Rightarrow x=\pm2\)
Thay x = 2 vào bt D có
\(D=12.4+12.2-3=69\)
Thay x = - 2 vào bt D ta có
\(D=12.4-12.2-3=21\)
1. a) \(( 5x-1)^2 - (5x-4) ( 5x+4) = 7\)
\(\Leftrightarrow\)\(25x^2-10x+1-(25x^2-16)=7\)
\(\Leftrightarrow\)\(25x^2-10x+1-25x^2+16-7=0\)
\(\Leftrightarrow\)\(10x=10\)
\(\Rightarrow x=1\)
b) \(( 4x-1)^2 - (2x+3)^2 + 5(x+2)^2 + 3(x-2) ( x+2) = 500\)
\(\Leftrightarrow\)\(16x^2-8x+1-4x^2-12x-9+5x+10+3x^2-12=500\)
\(\Leftrightarrow\)\(15x^2-15x=510\)
\(\Leftrightarrow\)\(15(x^2-x)=510\)
\(\Leftrightarrow\)\(x^2-x=34\)
\(\Rightarrow x=-5,352349955\)
c) \((x-2)^3 - (x-2) ( x^2+2x+4 ) + 6(x-2)(x+2) = 60\)
\(\Leftrightarrow x^3-6x^2+12x-8-\left(x^3-2^3\right)+6\left(x^2-4\right)=60\)
\(\Leftrightarrow x^3-6x^2+12x-8-x^3+8+6x^2-24=60\)
\(\Leftrightarrow12x-24=60\)
\(\Leftrightarrow12x=84\)
\(\Rightarrow x=7\)
a; A = (7\(x\) + 5)2 + (3\(x-5\))2 - (10 - 6\(x\)).(5 + 7\(x\))
A = 49\(x^2\) + 70\(x\) + 25 + 9\(x^2\) - 30\(x\) + 25 - 50 - 70\(x\) + 30\(x\) + 42\(x^2\)
A = (49\(x^2\) + 9\(x^2\) + 42\(x^2\)) + (70\(x-70x\)) - (30\(x\) - 30\(x\)) + (25+25-50)
A = 100\(x^2\) + 0 + 0 + (50 - 50)
A = 100\(x^2\) + 0 + 0 + 0
A = 100\(x^2\)
Thay \(x=-2\) vào A = 100\(x^2\) ta có:
A = 100.(-2)2
A = 100.4
A = 400.
a: Sửa đề: \(A=\left(3a-1\right)\left(9a^2+3a+1\right)-\left(3a+1\right)\left(9a^2-3a+1\right)+2a+2\)
\(=27a^3-1-27a^3-1+2a+2=2a=2\cdot5=10\)
b: \(=4x^2+2x+1-20x^3+10x^2+4x\)
\(=-20x^3+14x^2+6x+1\)
c: \(=5x^2-20xy-4y^2+20xy=5x^2-4y^2\)
\(=5\cdot\dfrac{1}{25}-4\cdot\dfrac{1}{4}=\dfrac{1}{5}-1=-\dfrac{4}{5}\)