Toán Lớp 7: Cho M=(x+y+z)/t = (y+z+t)/x = (z+t+x)/y = (t+x+y)/z (x, y, z, t $\neq$ 0)
Tính (M-1)^2020
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Toán Lớp 7: Cho M=(x+y+z)/t = (y+z+t)/x = (z+t+x)/y = (t+x+y)/z (x, y, z, t $\neq$ 0)
Tính (M-1)^2020
Comments ( 1 )
Ta có:
M+1 = (x+y+z)/t + 1 = (y+z+t)/x + 1=(z+t+x)/y +1= (t+x+y)/z + 1
= (x+y+z)/t + t/t = (y+z+t)/x + x/x = (z+t+x)/y + y/y = (t+x+y)/z + z/z
= (x+y+z+t)/t = (y+z+t+x)/x = (z+t+x+y)/y = (x+y+z+t)/z
=> t=x=y=z=a
=> M = (a+a+a)/a =(3a)/a = 3
=> (M-1)^2020 = (3-1)^2020 = 2^2020
Vậy (M-1)^2020 =2^2020