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Determinați numerele x,y,z, știind ca: a) xsupra2=y supra11=z supra7 si. X+y+z= 80
B)x supra6=y supra7=z supra 8 si x+y-z=20


Răspuns :

x/2=y/11=z/7=(x+y+z)/(2+11+7)=80/20=4
x/2=4⇒x=4*2=8
y/11=4⇒y=4*11=44
z/7=4⇒z=4*7=28

x/6=y/7=z/8=(x+y-z)/(6+7-8)=20/5=4
x/6=4⇒x=4*6=24
y/7=4⇒y=7*4=28
z/8=4⇒z=4*8=32
x/2=y/11=z/7 = k
x/2 = k, x = 2k
y/11 = k, y = 11k
z/7 = k, z = 7k
2k+11k+7k = 80
20k = 80
k = 80:20
k = 4
x = 2k = 2*4 = 8
y = 11k = 11*4 = 44
z = 7k = 7*4 = 28
B) x/6=y/7=z/8 = k
x/6 = k, x = 6k
y/7 = k, y = 7k
z/8 = k, z = 8k
6k+7k+8k = 20
21k = 20
k = 20:21
ai gresit ceva la punctul b deoarece nu iti da