Given: x2=17x+y and y2=x+17y,x≠y Formula Used: a2−b2=(a−b)(a+b) Calculation: We have x2=17x+y⋯−(i) y2=x+17y⋯( ii) On applying (i) - (ii), we get x2−y2=16x−16y ⇒(x−y)(x+y)=16(x−y) ⇒(x+y)=16 Now, On applying (i) + (ii), we get x2+y2=18x+18y ⇒x2+y2=18(x+y) ⇒x2+y2=18×16[ from (i)] ⇒x2+y2=288 Now, we have to find the value of √x2+y2+1 So, from equation (iv), we get ⇒√288+1=√289=17 ∴ The required value of √x2+y2+1 is 17 .