Question 762462

{{{3 + sqrt(z-7) = sqrt (z+8)}}}


{{{3 = sqrt (z+8)-sqrt(z-7) }}}.....square both sides


{{{3^2 = (sqrt (z+8)-sqrt(z-7))^2 }}}

{{{9 = (sqrt (z+8))^2-2sqrt (z+8)sqrt(z-7)+(sqrt(z-7))^2 }}}

{{{9 = z+8-2sqrt (z+8)sqrt(z-7)+z-7 }}}...........since {{{sqrt (z+8)sqrt(z-7)=sqrt((z+8)(z-7))}}}, we will have


{{{9 = 2z+1-2sqrt((z+8)(z-7)) }}}


{{{2sqrt((z+8)(z-7)) = 2z+1-9 }}}


{{{2sqrt((z+8)(z-7)) = 2z-8 }}}.... both sides divide by {{{2}}}

{{{sqrt((z+8)(z-7)) = z-4 }}}.....square both sides


{{{(sqrt((z+8)(z-7)))^2 = (z-4)^2 }}}

{{{(z+8)(z-7) = z^2-8z+16 }}}

{{{z^2+8z-7z-56 = z^2-8z+16 }}}

{{{cross(z^2)+z-56 = cross(z^2)-8z+16 }}}

{{{z-56 = -8z+16 }}}

{{{z+8z= 56+16 }}}

{{{9z= 72 }}}

{{{z= 72/9 }}}

{{{z= 8 }}}