Janek191:
a + b + c = 70
b = a + 1
a
2 + b
2 = c
2
−−−−−−−−−−−−
to
a + ( a + 1) + c = 70
2 a + c = 69
c = 69 − 2a
więc
a
2 + ( a + 1)
2 = ( 69 − 2 a)
2
a
2 + a
2 + 2 a + 1 = 4 761 − 276 a + 4 a
2
2 a
2 − 278 a + 4 760 = 0 / : 2
a
2 − 139 a + 2 380 = 0
Δ = ( − 139)
2 − 4*1*2 380 = 19 321 − 9 520 = 9 801
√Δ = 99
| | 139 − 99 | | 139 + 99 | |
a = |
| = 20 lub a = |
| = 119 > 70 − odpada |
| | 2 | | 2 | |
b = a + 1 = 21
c = 69 − 2 a= 69 − 2*20 = 29
Odp.
a = 20 cm, b = 21 cm, c = 29 cm
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