Question

se da: a/x=b/y=c/z=6. calculati  a) a+b+c/ x+y+z     b) 3a+4b+5c/3x+4y+5z                               c) a la 2 + b la 2+ c la 2/ x la 2+y la 2 +z la 2    d) a la n+ b la n + c la n/ x la n+ b la n+ z la n   ( n apartinand N*)      e) ma+nb+pc/mx+ny+pz    (n, m , p apartinand N*)

Answer 1

a)   a/x = b/y = c/z = (a+b+c)/(x+y+z) =6

b)  3a/3x = 4b/4y =5c/5z =6 = (3a+4b+5c)/(3x+4y+5z)

c)  a²/x² = b²/y² = c²/z²=36 = (a²+b²+c²)/(x²+y²+z²)

d)  (a/x)^n = (b/y)^n =(c/z)^n =6^n ⇒ (a^n + b^n +c^n)/(x^n +y^n +z^n)=6^n

e)  (ma)/(mx) = (nb)/(ny) = (pc)/(pz) = a/x =b/y =c/z =6=                             (a+b+c)/(x+y+z)  ⇒ (ma+nb+pc)/(mx+ny+pz) = 6             

Answer 2

a) a/x=b/y=c/z=(a+b+c)/(x+y+z)=6
b) 3a/3x=4b/4y=5c/5z=(3a+4b+5c)/(3x+4y+5z)=6
c)a/x=b/y=c/z=6⇒ a^2/x^2=b^2/y^2=c^2/z^2 =(a^2+b^2+c^2)/(x^2+y^2+z^2)=36
d)a^n/x^n=b^n/y^n=c^n/z^n=(a^n+b^n+c^n)/(x^n+y^n+z^n)=6^n
e)ma/mx=nb/ny=pc/pz=(ma+nb+zc)/(mx+ny+pz)=6