#sqrt(y-10)-1=4#
#sqrt(y-10)-1-4=0#
#sqrt(y-10)-5=0#
To solve #y# we should get rid of the square root by multiplying by its conjugate that is #color(red)(sqrt(y-10)+5)#
#(sqrt(y-10)-5)*1=0#
#(sqrt(y-10)-5)*color(red)((sqrt(y-10)+5)/(sqrt(y-10)+5))=0#
#((sqrt(y-10)-5)*(sqrt(y-10)+5))/(sqrt(y-10)+5)=0#
The product of #((sqrt(y-10)-5)*(sqrt(y-10)+5))#is determined by applying the polynomial identity
#color(blue)(a^2-b^2=(a-b)(a+b))#
#color(blue)(((sqrt(y-10))^2-5^2))/(sqrt(y-10)+5)=0#
#rArr(y-10-25)/(sqrt(y-10)+5)=0#
#rArr(y-35)/(sqrt(y-10)+5)=0#
A fraction is equal to zero when its numerator is zero
#rArry-35=0#
Therefore, #y=35#
