Tính:
(x-y)*(x+y)*(y-z)*(y+z)
Những câu hỏi liên quan
x/y+z+t = y/x+t+z = z/x+y+t = t/x+y+z . Tính P = x+y / z+t + y+z/t+x + z+t/x+y + t+x / y+z
Cho 1/x+y +1/y+z +1/z+x=0 Tính P=(y+z)(z+x)/(x+y)^2 + (x+y)(z+x)/(y+z)^2+ (y+z)(x+y)/(z+x)^2
Đặt \(\dfrac{1}{a}=\dfrac{1}{x+y},\dfrac{1}{b}=\dfrac{1}{y+z},\dfrac{1}{c}=\dfrac{1}{z+x}\)
Đề trở thành: \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=0\), tính \(P=\dfrac{bc}{a^2}+\dfrac{ac}{b^2}+\dfrac{ab}{c^2}\)
\(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=0\) Tương đương \(ab+bc=-ac\)
\(P=\dfrac{b^3c^3+a^3c^3+a^3b^3}{a^2b^2c^2}=\dfrac{\left(ab+bc\right)\left(a^2b^2-ab^2c+b^2c^2\right)+a^3c^3}{a^2b^2c^2}=\dfrac{-ac\left(a^2b^2-ab^2c+b^2c^2\right)+a^3c^3}{a^2b^2c^2}\)
\(=\dfrac{a^2c^2-a^2b^2+ab^2c-b^2c^2}{ab^2c}=\dfrac{ac}{b^2}-\dfrac{a}{c}+1-\dfrac{c}{a}\)\(=ac\left(\dfrac{1}{a^2}+\dfrac{2}{ac}+\dfrac{1}{c^2}\right)-\dfrac{a}{c}+1-\dfrac{c}{a}\) (do \(\dfrac{1}{b}=-\dfrac{1}{a}-\dfrac{1}{c}\) tương đương \(\dfrac{1}{b^2}=\dfrac{1}{a^2}+\dfrac{2}{ac}+\dfrac{1}{c^2}\))
\(=3\)
Vậy P=3
Đúng 0
Bình luận (0)
Cho x+y+z=0
Tính P= (x-y/z + y-z/x + z-x/y)(z/x-y + x/y-z + y/z-x)
y+z-x/x=z+x-y/y=x+y-z/z
tính B=(1+x/y).(1+y/z).(1+z/y)
Biết x/y=z+t=y/z+t+x=z/t+x+y=t/x+y+z
Tính P=x+y/z+t +y+z/t+x +z+t/x+y +t+x/y+z
tính
P=x+y/z+t+y+z/t+x+z+t/x+y+t+x/y+z
biết x/y+z+t=y/z+t+x=z/t+x+y=t/x+y+z
kím đâu ra mí bài này zậy bạn? chỉ mik nhé
Đúng 0
Bình luận (0)
сho (x ^ 2)/(x + y) + (y ^ 2)/(y + z) + (z ^ 2)/(z+ x) = 2000 tính (y ^ 2)/(x + y) + (z ^ 2)/(y + z) + (x ^ 2)/(z+ x)
сho (x ^ 2)/(x + y) + (y ^ 2)/(y + z) + (z ^ 2)/(z+ x) = 2000 tính (y ^ 2)/(x + y) + (z ^ 2)/(y + z) + (x ^ 2)/(z+ x)
x/(y+z) +y/(x+z)+z/(x+y)=1
Tính x^2(y+z)+y^2/(x+z)+z^2/(x+y)
cho x/z+t=y+z/t+x=z+t/x+y=t/x+y+z
Tính P= x+y/z+t + y+z/t+x + z+t/x+y + t+x/z+y