Question

Zapisz i rozwiaz odpowiedni uklad rownan.
pole = 126
obwod = 54

Answer 1

Ab=126
2a+2b=54 /:2

ab=126
a+b=27→a=27-b

b(27-b)=126
-b²+27b-126=0

Δ=b²-4ac=729-504=225
√Δ=15

b₁=(-b-√Δ):2a=(-27-15):-2=21
b₂=(-b+√Δ):2a=(-27+15):-2=6

a₁=27-b=27-21=6
a₂=27-6=21


spr. ab=126
21×6=126
126=126


2a+2b=54
2×6+2×21=54
54=54

Answer 2

( a*b = 126
( 2a + 2b = 54 /:2

( a*b = 126
( a + b = 27

( a*b = 126
( a = 27 - b

( (27-b)*b = 126
( a = 27 - b

( 27b - b² = 126
( a = 27 - b

( -b² + 27b - 126 = 0
( a = 27 - b

[delta = d]

d =729 - 4 *(-) * (-126)
d = 729 - 504
d = 225
√d = 15

b₁ = -b - √d /2a
b₁ = -27 + 15 /-2 = -42 /-2 = 21

b₂ = -27+ 15 /-2 = -2/-2 = 1

[ b₂ nie spełnia warunków zadania, ponieważ 1* 26 jest spełnia wrunków zadania]

( b = 21
( a = 27 - b

( b = 21
( a = 27 -21

( b = 21
( a = 6