Cho 2 so thuc a, b thoa man dieu kien ab= 1, a+ b\(\ne\)0. Tinh gia tri bieu thuc :

P= \(\frac{1}{\left(a+b\right)^3}\left(\frac{1}{a^3}+\frac{1}{b^3}\right)+\frac{3}{\left(a+b\right)^4}\left(\frac{1}{a^2}+\frac{1}{b^2}\right)+\frac{6}{\left(a+b\right)^3}\left(\frac{1}{a}+\frac{1}{b}\right)\)

Chung minh bieu thuc sau ko phu thuoc vao gia tri cua x:

\(A=\dfrac{6x-\left(x+6\right)\sqrt{x}-3}{2\left(x-4\sqrt{x}+3\right)\left(2-\sqrt{x}\right)}-\dfrac{3}{-2x+10\sqrt{x}-12}-\dfrac{1}{3\sqrt{3}-x-2}\)

tính giá trị của\(\dfrac{a^2\left(a^2+b^2\right)\left(a^4+b^4\right)\left(a^8+b^8\right)\left(a^3-3b\right)}{a^{10}++b^{10}}\):

A= tại a=6;b=12

Cho bieu thuc:P=\(\dfrac{\left(a+3\right)^2}{a^2+3a}\times\left(1-\dfrac{6a-18}{a^2-9}\right)\)voi a ≠0;a≠ +-3

a)rut gon bieu thuc P

b)tim gia tri cua a de P= -2

c)tim cac gia tri nguyen cua a de bieu thuc P co gia tri nguyen

mng giup minh voi mai thi rui!

a, biet x+y=0

tinh gia tri bieu thuc : M=\(x^4-xy^3+x^3y-y^4-1\)

b, biet xyz=2 va x+y+z=0

tinh gia tri bieu thuc : M= \(\left(x+y\right)\left(y+2\right)\left(x+2\right)\)

7 Chứng minh các đẳng thức sau

a) \(a^2+b^2=\left(a+b\right)^2-2ab\) ; b) \(a^4+b^4=\left(a^2+b^2\right)^2-2a^2b^2\)

c) \(a^6+b^6=\left(a^2+b^2\right)\left[\left(a^2+b^2\right)^2-3a^2b^2\right]\)

d) \(a^6-b^6=\left(a^2-b^2\right)\left[\left(a^2+b^2\right)^2-a^2b^2\right]\)

Cho bieu thuc: \(Q=\left(\dfrac{x^2-2x}{2x^2+8}+\dfrac{2x^2}{x^2.\left(x-2\right)}\right).\left(\dfrac{x^2-x-2}{x^2}\right)\)

a, Rut gon bieu thuc Q

b, Tim gia tri ca x de Q co gia tri bang \(\dfrac{1}{4}\)

A=\(\frac{\left(1^3+2^3+3^3+...+10^3\right)\cdot\left(x^2+y^2\right)\cdot\left(x^3+y^3\right)\cdot\left(x^4+y^4\right)}{1^2+2^2+3^2+...+10^2}\)

Tinh gia tri bieu thuc

Tim gia tri nho nhat cua bieu thuc :

a)A=\(\left|x+5\right|+2-x\)

b)B=\(\left|x-1\right|+x+6\)