Question

to
If
x² + y² + z² = 70
x+y+z = 12 :
xy + Y Z + ZX = 37
then find X, Y, Z
​

Answer 1

Step-by-step explanation:

Given If

x² + y² + z² = 70  x+y+z = 12  find x^3 + y^3 + z^3 – 3 xyz

• Given x + y + z = 12 and x^2 + y^2 + z^2 = 70
• We know that (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca  can be used
• We can write as (x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx
•              So (12)^2 = 70 + 2(xy + yz + zx)
•           So 144 = 70 + 2(xy + yz + zx)
•       So xy + yz + zx = 144 – 70 / 2
•      Or xy + yz + zx = 37
• Now x^3 + y^3 + z^3 – 3 xyz = (x + y + z)(x^2 + y^2 + z^2 – xy – yz – zx)
•                                                = 12 (70  – (xy + yz + zx)
•                                              = 12 (70  - 37)
•                                                 = 12 x 33
•                                                 = 396
• Now x^3 + y^3 + z^3 – 3xyz = 396  

Reference link will be

https://brainly.in/question/1031544