Question

Please answer my questions
If x^2+y^2+z^2=40 and xy+yz+zx=30 find X+y+z

Answer 1

Answer:

x + y + z = ± 10

Step-by-step explanation:

Given :

x² + y² + z² = 40,

xy + yz + zx = 30,

Find :

x + y + z,.

Solution :

We know that,

(a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc,

By substituting,

a = x , b = y , c = z,

We get,

⇒ (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2xz

⇒ (x + y + z)² = (x² + y² + z²) + 2(xy + yz + xz)

⇒ (x + y + z)² = (40) + 2(30)

⇒ (x + y + z)² = (40) + (60)

⇒ (x + y + z)² = 100

⇒ x + y + z = ± 10  (by taking square root both the sides, 10 × 10 = 100, -10 × -10 = 100)