If x^2 + y^2 + z^2 = 70, x + y + z = 12, xy + yz + zx = 37 then find x, y and z
Answers
Given : x² + y² + z² = 70, x + y + z = 12, xy + yz + zx = 37
To find : x, y and z
Solution:
(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)
=> 12² = 70 + 2(37)
=> 144 = 70 + 74
=> 144 = 144
Hence 3rd Equation can be found if 2 Equations are given
Hence these 3 Equations are basically 2 Equations
and 3 Variable x , y & z
We can not solve 3 variables with 2 Equations
There can be many possible solutions
few are below :
x = √37 i y = -√37 i z = 12
x = -√37 i y = √37 i z = 12
z= √37 i y = -√37 i x = 12
z = -√37 i y = √37 i x = 12
x = √37 i z = -√37 i y = 12
x = -√37 i z = √37 i y = 12
Verification
x² + y² + z² = -37 - 37 + 144 = 70 (i² = -1)
x + y + z = √37 i -√37 i + 12 = 12
xy + yz + zx = (√37 i) * (-√37 i) + (√37 i) 12 + (-√37 i) 12 = 37
Not Enough Details to find Unique Solutions
Learn more:
if x+y+z=0 then the square of the value of (x+y)^2/xy+(y+z)^2/yz+(z+x)
https://brainly.in/question/12858114
Find x,y,z using cramers rule, if x-y+z=4, 2x+y-3z=0 and x+y+z=2
https://brainly.in/question/9052437