If positive integers satisfying \[ \begin{array}{r} (1+x)(1+y)=4 y \\ (1+y)(1+z)=4 z \\ (1+z)(1+x)=4 x \end{array} \] \[ (1+z)(1+x)=4 x \text {. then the value of } \] \( 2 x+3 y+4 z+x^{2}+y^{3}+z^{4} i \) is

Question

If positive integers satisfying: (l+x)(l+y)=4y

   (l+y)(l+z)=4z

(l+z)(l+x)=4x then the value of 2x+3y+4z+x²+y²+z⁴ is 

Answer 1

All equations (1 + x)(1 + y) = 4y

(1 + y) (1 + z) = 4z

(1 + z) (1 + x) = 4x

will satisfy by x = y = z = 1

\(\therefore\) 2x + 3y + 4z + x² + y³+z⁴ 

 = 2 + 3 + 4 + 1 + 1 + 1 = 12