If ⁻¹ x+ ⁻¹ y+ ⁻¹ z= and x^2+y^2+z^2+k x y z=1 , then k is

Step-by-step solution

aligned & Given, ⁻¹ x+ ⁻¹ y+ ⁻¹ z= & ⁻¹ x+ ⁻¹ y= - ⁻¹ z & ⁻¹ x+ ⁻¹ y= ⁻¹(-z) & ⁻¹ [x y- ( 1-x^2 ) ( 1-y^2 ) ]= ⁻¹-z & x y- (1-x^2 ) (1-y^2 ) =-z & x y+z= (1-x^2 ) (1-y^2 ) aligned array ll & Squaring on both sides & x^2 y^2+2 x y z+z^2= (1-x^2 ) (1-y^2 ) & x^2 y^2+2 x y z+ z ^2=1-y^2-x^2+x^2 y^2 & x^2+y^2+ z ^2+2 x y z =1 & But x^2+y^2+ z ^2+ kxyz =1 k =2 array