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{x,y,z} i.p. {0.(3) ; 0.25 ; 0.2}

a) verificati daca x la puterea a doua + y la puterea a doua = z la puterea a doua

b) Demonstrati ca 2x + 2z supra 5y + z = patrat perfect

c) Aflati cele 3 numere stiind ca 3 supra x + 4 supra y + 5 supra z = 1



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Răspuns :

0,(3)=3/9=1/3
1/1/3=3
0,25=25/100=1/4
1/1/4=4
0,2=2/10=1/5
1/1/5=5
x/3=y/4=z/5=k
x=3k
y=4k
z=5k
x^2+y^2=z^2
9k^2+16k^2=25k^2
b)2×3k+2×5k/5×4k+5k=16k/25k=16/25=(4/5)^2
c)3/3k+4/4k+5/5k=1
1/k+1/k+1/k=1
3/k=1
k=3
x=3×3=9
y=4×3=12
z=5×3=15

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