Question

8. Si: a + b + c = 10
a² + b² + c² = 40
calcular el valor de:
P = (a + b)² + (a + c)² + (b + c)²
a) 110
b) 100
d) 140
c) 70
9. Si: a,b,c € R; además:
a? + b2 + c2 = ab + bc + ac
Calcule el valor de:
a3 + b3
M=
C3​

Answer 1

Explicación paso a paso:

8)

(a+b+c)^2 = (10)^2

a² + b² + c² + 2ab + 2ac + 2bc = 100

40 + 2(ab + bc + ac) = 100

ab + bc + ac = 30

(a + b)² + (a + c)² + (b + c)²

a² + b² + 2ab + a² + c² + 2ac + b² + c² +2bc

2(a² + b² + c²) + 2(ab+ac+bc)

2(40) + 2(30)

80 + 60

140