x^2-7X+10/X^2-5x
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1, \(A=5x\left(x^2-3\right)+x^2\left(7-5x\right)-7x^2\)
\(A=5x^3-15x+7x^2-5x^3-7x^2\)
\(A=\left(5x^3-5x^3\right)+\left(7x^2-7x^2\right)-15x\)
\(A=-15x\)
Thay \(x=-5\) vào A ta được:
\(-15\cdot-5=75\)
Vậy: ....
2. \(B=x\left(x^2-3\right)+x^2\left(7-5x\right)-7x^2\)
\(B=x^3-3x+7x^2-5x^3-7x^2\)
\(B=\left(x^3-5x^3\right)+\left(7x^2-7x^2\right)-3x\)
\(B=-4x^3-3x\)
Thay \(x=10,y=-1\) vào B ta được:
\(-4\cdot10^3-3\cdot10=-4\cdot1000-3\cdot10=-4000-30=-4030\)
Vậy: ....
1) x2 -7x + 10 = x2 - 2x - 5x + 10 = x(x - 2) - 5(x - 2) = (x - 5)(x - 2)
2) x2 + 3x + 2 = x2 + 2x + x + 2 = x(x + 2) + (x + 2) = (x + 1)(x + 2)
3) x2 - 7x + 12 = x2 - 3x - 4x + 12 = x(x - 3) - 4(x - 3) = (x - 3)(x - 4)
4) x2 + 7x + 12 = x2 + 3x + 4x + 12 = x(x + 3) + 4(x + 3) = (x + 3)(x + 4)
5) 16x - 5x2 - 3 = 15x - 5x2 + x - 3 = -5x(x - 3) + (x - 3) = (x - 3)(1 - 5x)
6) 6x2 + 7x - 3 = 6x2 - 2x + 9x - 3 = 2x(3x - 1) + 3(3x - 1) = (2x + 3)(3x - 1)
7) 3x2 - 3x - 6 = 3x2 - 6x + 3x - 6 = 3x(x - 2) + 3(x - 2) = (x - 2)(3x + 3) = 3(x - 2)(x + 1)
8) 3x2 + 3x - 6 = 3x2 - 3x + 6x - 6 = 3x(x - 1) + 6(x - 1) = (x - 1)(3x + 6) = 3(x - 1)(x + 2)
9) 6x2 - 13x + 6 = 6x2 - 9x - 4x + 6 = 3x(2x - 3) - 2(2x - 3) = (3x - 2)(2x - 3)
10) 6x2 + 15x + 6 = 6x2 + 12x + 3x + 6 = 6x(x + 2) + 3(x + 2) = (x + 2)(6x + 3) = 3(x + 2)(3x + 1)
11) 6x2 - 20x + 6 = 6x2 - 18x - 2x + 6 = 6x(x -3) - 2(x - 3) = (6x - 2)(x - 3) = 2(3x - 1)(x - 3)
12) 8x2 + 5x - 3 = 8x2 + 8x - 3x - 3 = 8x(x + 1) - 3(x + 1) = (x + 1)(8x - 3)
\(=\lim\limits_{x\rightarrow0}\dfrac{x^2\left(x^6-3x^4+5x^2+1\right)}{x^2\left(3x^8-7x^3+5\right)}=\lim\limits_{x\rightarrow0}\dfrac{x^6-3x^4+5x^2+1}{3x^8-7x^3+5}=\dfrac{0-0+0+1}{0-0+5}\)
2: =(2x+1)^2-y^2
=(2x+1+y)(2x+1-y)
3: =x^2(x^2+2x+1)
=x^2(x+1)^2
4: =x^2+6x-x-6
=(x+6)(x-1)
5: =-6x^2+3x+4x-2
=-3x(2x-1)+2(2x-1)
=(2x-1)(-3x+2)
6: =5x(x+y)-(x+y)
=(x+y)(5x-1)
7: =2x^2+5x-2x-5
=(2x+5)(x-1)
8: =(x^2-1)*(x^2-4)
=(x-1)(x+1)(x-2)(x+2)
9: =x^2(x-5)-9(x-5)
=(x-5)(x-3)(x+3)
a) \(P=5x\left(x^2-3\right)+x^2\left(7-5x\right)-7x^2\)
\(=5x^3-15x+7x^2-5x^3-7x^2\)
\(=-15x\)
Tại x = -5, ta có:
-15. (-5) = 75
b) \(Q=x\left(x-y\right)+y\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y\right)\)
\(=x^2-y^2\)
Tại x = 1,5 và y = 10, ta có:
\(1,5^2-10^2=\frac{9}{4}-100=-\frac{391}{4}\)