Question

Si a + b + c = 12 y ab=10 bc=20 y ac=15
CUAL ES EL VALOR DE

a^2+b^2+c^2=?

Ayuda pls

Answer 1

Dados a+b+c = 12 y ab = 10, bc =20 y ac = 15.

El valor de a²+b²+c² es:

a²+b²+c² = 305/6

Explicación:

ab = 10

despejar a;

a = 10/b

bc = 20

despejar b;

b = 20/c

ac = 15

Sustituir a;

10/b × c = 15

sustituir b;

(10/20)c × c = 15

(1/2)c² = 15

Despejar c;

c² = 15 × 2

c² = 30

ab = 10

sustituir b;

a × 20/c = 10

sustituir c;

a × (20/15)a = 10

(4/3)a² = 10

a² = 10(3/4)

a² = 15/2

bc = 20

sustituir c;

b × 15/a = 20

sustituir a;

b × (15/10)b = 20

(3/2)b² = 20

b² = 20(2/3)

b² = 40/3

 

a²+b²+c² = 15/2 + 30 + 40/3

a²+b²+c² = 305/6