Question

If x^2+y^2+z^2=70
X+y+z=12
xy+yz+zx=37
Then find the value of x,y,z

Answer 1

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

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