Решите систему уравнений. Created by haydeggerdi1. algebra-ru

Решите систему уравнений...

haydeggerdi1 @haydeggerdi1

December 2021 1 5 Report

Решите систему уравнений

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mikael2

Verified answer

Xy+x+y=15
x²y+y²x=54 xy(x+y)=54

54/(x+y)+(x+y)=15 x+y=z 54/z +z=15 54+z²-15z=0
z²-15z+54=0 D=225-4*54=225-216=9
z1=1/2[15+3]=9
z2=1/2[15-3]=6

z=9 xy=15-9=6
x+y=9 x+6/x=9 x²-9x+6=0 D=81-24=57 x=1/2[9+√57] y=9-1/2[9+√57]
x+y=6 xy=9 x+9/x=6 x²-6x+9=0 (x-3)²=0 x=3 y=6/3=2

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2^(√x+√y)=512 512=2^9 → √x+√y=9
lg√xy=1/2*lg400 1/2*lg400=lg√400=lg20

√xy=20
√x+√y=9

√x=t √y=p
tp=20
t+p=9 t+20/t=9 t²-9t+20=0 корни по Виету 4 и 5
t=4 p=5 √x=4 x=16 y=25
t=5 p=4 √x=5 x=25 y=16

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