Question 919361
{{{(x+y)^2 + (4x-7y)^2 + 10=9}}} 

to find {{{x}}} intercepts, set {{{y=0}}}


{{{(x+0)^2 + (4x-7*0)^2 + 10=9}}} 


{{{x^2 + (4x)^2 =9-10}}} 

{{{x^2 + 16x^2 =-1}}}

{{{17x^2 =-1}}}

{{{x^2 =-1/17}}}

{{{x =sqrt(-1/17)}}}

{{{x =sqrt(-1)/sqrt(17)}}}

solutions:

{{{x =i/sqrt(17)}}} or {{{x =-i/sqrt(17)}}}..... complex root, no real solution

  



to find {{{y}}} intercepts, set {{{x=0}}}


{{{(0+y)^2 + (4*0-7y)^2 + 10=9}}} 


{{{y^2 + (-7y)^2 =9-10}}} 

{{{y^2 + 49y^2 =-1}}}

{{{50y^2 =-1}}}

{{{y^2 =-1/50}}}

{{{y =sqrt(-1/50)}}}

{{{y =sqrt(-1)/sqrt(50)}}}

solutions:

{{{y =i/sqrt(50)}}} or {{{y =-i/sqrt(50)}}} .... complex root, {{{no}}}{{{ real}}} solution

so, there is  neither an {{{x}}} nor a {{{y}}} intercept intercepts