\(x^2-2\) 

\(y^2-13\)

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\(x^2-2\)

\(=x^2-\left(\sqrt{2}\right)^2\)

\(=\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)

\(y^2-13\)

\(=y^2-\left(\sqrt{13}\right)^2\)

\(=\left(y-\sqrt{13}\right)\left(y+\sqrt{13}\right)\)

19 tháng 7 2017

a)Tại \(x=87;y=13\) thì

\(A=x^2-y^2=\left(x-y\right)\left(x+y\right)\)

\(=\left(87-13\right)\left(87+13\right)=74\cdot100=7400\)

b)Tại \(x=\dfrac{1}{3}\) thì

\(B=9x^2-6x+1=\left(x-\dfrac{1}{3}\right)^2\)

\(=\left(\dfrac{1}{3}-\dfrac{1}{3}\right)^2=0^2=0\)

c)Tại \(x=1;y=2\) thì

\(C=4x^2-12xy+9y^2=\left(2x-3y\right)^2\)

\(=\left(2\cdot1-3\cdot2\right)^2=\left(-4\right)^2=16\)

19 tháng 7 2017

a, Ta có:

\(A=x^2-y^2=\left(x-y\right)\left(x+y\right)\)

Thay \(x=87;y=13\) vào A ta được:

\(\left(87-13\right)\left(87+13\right)=74.100=7400\)

b, Ta có:

\(B=9x^2-6x+1=9x^2-3x-3x+1\)

\(=3x\left(3x-1\right)-\left(3x-1\right)\)

\(=\left(3x-1\right)^2\)

Thay \(x=\dfrac{1}{3}\) vào B ta được:

\(\left(3.\dfrac{1}{3}-1\right)^2=0\)

c, Ta có:

\(C=4x^2-12xy+9y^2=4x^2-6xy-6xy+9y^2\)

\(=2x\left(2x-3y\right)-3y\left(2x-3y\right)\)

\(=\left(2x-3y\right)^2\)

Thay \(x=1;y=2\) vào biểu thức C ta được:

\(\left(2.1-3.2\right)^2=\left(2-6\right)^2=\left(-4\right)^2=16\)

Chúc bạn học tốt!!!

20 tháng 10 2020

Câu 1) xem lại đề giùm đi em.

29 tháng 6 2017

8) \(y^2-y-30=y^2+5y-6y-30=y\left(y+5\right)-6\left(y+5\right)=\left(y-6\right)\left(y+5\right)\)

9) \(y^2-8y+15=y^2-3y-5y+15=y\left(y-3\right)-5\left(y-3\right)=\left(y-5\right)\left(y-3\right)\)

10) \(y^2+y-6=y^2-2y+3y-6=y\left(y-2\right)+3\left(y-2\right)=\left(y+3\right)\left(y-2\right)\)

11) \(y^2-y-12=y^2+3y-4y-12=y\left(y+3\right)-4\left(y+3\right)=\left(y-4\right)\left(y+3\right)\)

12) \(x^2-5x+6=x^2-2x-3x+6=x\left(x-2\right)-3\left(x-2\right)=\left(x-3\right)\left(x-2\right)\)

13) \(u^2+u-42=u^2+7u-6u-42=u\left(u+7\right)-6\left(u+7\right)=\left(u-6\right)\left(u+7\right)\)

29 tháng 6 2017

14) \(2x^2+x-6=2x^2+4x-3x-6=2x\left(x+2\right)-3\left(x+2\right)=\left(2x-3\right)\left(x+2\right)\)

15) \(7x^2+50x+7=7x^2+49x+x+7=7x\left(x+7\right)+\left(x+7\right)=\left(7x+1\right)\left(x+7\right)\)

16) \(12x^2+7x-12=12x^2+16x-9x-12=4x\left(3x+4\right)-3\left(3x+4\right)=\left(4x-3\right)\left(3x+4\right)\)

17) \(15x^2+7x-2=15x^2-3x+10x-2=3x\left(5x-1\right)+2\left(5x-1\right)=\left(3x+2\right)\left(5x-1\right)\)

18) \(2x^2-y^2+xy=2x^2+2xy-xy-y^2=2x\left(x+y\right)-y\left(x+y\right)=\left(2x-y\right)\left(x+y\right)\)

19) \(x^2-3xy+2y^2=x^2-xy-2xy+2y^2=x\left(x-y\right)-2y\left(x-y\right)=\left(x-2y\right)\left(x-y\right)\)

29 tháng 10 2017

1,Thực hiện phép tính :

a, (x + 2)9 : (x + 2)6

=(x+2)9-6

=(x+2)3

b, (x - y) 4 : (x - 2)3

=(x-y)4-3

=x-y

c, ( x2+ 2x + 4)5 : (x2 + 2x + 4)

=(x2+2x+4)5-1

=(x2+2x+4)4

d, 2(x2 + 1)3 : 1/3(x2 + 1)

=(2÷1/3).[(x2+1)3÷(x2+1)]

=6(x2+1)2

e, 5 (x - y)5 : 5/6 (x - y)2

=(5÷5/6).[(x-y)5÷(x-y)2]

=6(x-y))3

6 tháng 6 2017

\(a,x^2-y^2=\left(x+y\right)\left(x-y\right)=\left(87+13\right)\left(87-13\right)=100.74=7400\)\(b,x^3-3x^2+3x-1=\left(x-1\right)^3=\left(101-1\right)^3=100^3=1000000\)c,\(x^3+9x^2+27x+27=\left(x+3\right)^3=\left(97+3\right)^3=1000000\)

11 tháng 6 2017

a) x2 - y2 = (x+y)(x-y)

Thay x=87; y=13 có:

(87+13)(87-13) = 100.74 = 7400

b)x3-3x2+3x-1 = x3 - 3x2.1+ 3x .12 -13 = (x-1)3

Thay x=101 có:

(101-1)3 =1003 =1000000

c)x3+9x2+27x+27= x3 +3x2.1+3x.12+33= (x+3)3

Thay x=97 có:

(97+3)3= 1003=1000000

12 tháng 9 2017

a) x2 - y2 = ( x+y )( x-y )
Thay x = 87 và y = 13 vào biểu thức a) ta có :
( 87+13 )( 87-13 ) = 100.74 = 7400

12 tháng 9 2017

b) x3 - 3x2 + 3x -1 = x3 - 3x2.1 + 3x.12 - 13
= ( x - 1 )3
Thay x = 101 vào biểu thức b) ta có :
( 101 - 1 )3 = 1003 = 1000000

7 tháng 7 2017

Tất cả dùng công thức là A2 – B2= (A-B)(A+B)

1, Thực hiện phép tính : a, \(\dfrac{2x+4}{10}\) + \(\dfrac{2-x}{15}\) b, \(\dfrac{3x}{10}\) + \(\dfrac{2x-1}{15}\) + \(\dfrac{2-x}{20}\) c, \(\dfrac{x+1}{2x-2}\) + \(\dfrac{x^2+3}{2-2x^2}\) d, \(\dfrac{1-2x}{2x}\) + \(\dfrac{2x}{2x-1}\) + \(\dfrac{1}{2x-4x^2}\) e, \(\dfrac{x}{xy-y^2}\) + \(\dfrac{2x-y}{xy-x^2}\) f, \(\dfrac{x^2}{x^2-4x}\) + \(\dfrac{6}{6-3x}\) +\(\dfrac{1}{x+2}\) g, \(\dfrac{2x^2-10xy}{2xy}\) + \(\dfrac{5y-x}{y}\) + \(\dfrac{x+2y}{x}\) h, \(\dfrac{2}{x+y}\)...
Đọc tiếp

1, Thực hiện phép tính :

a, \(\dfrac{2x+4}{10}\) + \(\dfrac{2-x}{15}\)

b, \(\dfrac{3x}{10}\) + \(\dfrac{2x-1}{15}\) + \(\dfrac{2-x}{20}\)

c, \(\dfrac{x+1}{2x-2}\) + \(\dfrac{x^2+3}{2-2x^2}\)

d, \(\dfrac{1-2x}{2x}\) + \(\dfrac{2x}{2x-1}\) + \(\dfrac{1}{2x-4x^2}\)

e, \(\dfrac{x}{xy-y^2}\) + \(\dfrac{2x-y}{xy-x^2}\)

f, \(\dfrac{x^2}{x^2-4x}\) + \(\dfrac{6}{6-3x}\) +\(\dfrac{1}{x+2}\)

g, \(\dfrac{2x^2-10xy}{2xy}\) + \(\dfrac{5y-x}{y}\) + \(\dfrac{x+2y}{x}\)

h, \(\dfrac{2}{x+y}\) +\(\dfrac{1}{x-y}\) + \(\dfrac{-3x}{x^2-y^2}\)

i, x+y+ \(\dfrac{x^2+y^2}{x+y}\)

2, Thực hiện phép tính :

a, \(\dfrac{2x}{x^2+2xy}\) + \(\dfrac{y}{xy-2y^2}\)+ \(\dfrac{4}{x^2-4y^2}\)

b, \(\dfrac{1}{x-y}\) + \(\dfrac{3xy}{y^3-x^3}\) + \(\dfrac{x-y}{x^2+xy+y^2}\)

c, \(\dfrac{2x+y}{2x^2-xy}\) + \(\dfrac{16x}{y^2-4x^2}\) + \(\dfrac{2x-y}{2x^2+xy}\)

d, \(\dfrac{1}{1-x}\) +\(\dfrac{1}{1+x}\) + \(\dfrac{2}{1+x^2}\) + \(\dfrac{4}{1+x^4}\) + \(\dfrac{8}{1+x^8}\)+ \(\dfrac{16}{1+x^{16}}\)

1
13 tháng 11 2017

Bài 2 .

a) \(\dfrac{2x}{x^2+2xy}+\dfrac{y}{xy-2y^2}+\dfrac{4}{x^2-4y^2}\)

\(=\dfrac{2x}{x\left(x+2y\right)}+\dfrac{y}{y\left(x-2y\right)}+\dfrac{4}{\left(x-2y\right)\left(x+2y\right)}\)

\(=\dfrac{2xy\left(x-2y\right)+xy\left(x+2y\right)+4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)

\(=\dfrac{2x^2y-2xy^2+x^2y+2xy^2+4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)

\(=\dfrac{3x^2y+4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)

b) Sai đề hay sao ý

c) \(\dfrac{2x+y}{2x^2-xy}+\dfrac{16x}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\)

\(=\dfrac{2x+y}{x\left(2x-y\right)}+\dfrac{-16x}{\left(2x-y\right)\left(2x+y\right)}+\dfrac{2x-y}{x\left(2x+y\right)}\)

\(=\dfrac{\left(2x+y\right)^2-16x^2+\left(2x-y\right)^2}{x\left(2x-y\right)\left(2x+y\right)}\)

\(=\dfrac{4x^2+4xy+y^2-16x^2+4x^2-4xy+y^2}{x\left(2x-y\right)\left(2x+y\right)}\)

\(=\dfrac{-8x^2}{x\left(2x-y\right)\left(2x+y\right)}\)

d) \(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{2}{1-x^2}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{4}{1-x^4}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)

.....

\(=\dfrac{16}{1-x^{16}}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{32}{1-x^{32}}\)