Question 1131442
a)
{{{sqrt(q+2)=7 }}}.......square both sides

{{{(sqrt(q+2))^2=7^2 }}}

{{{q+2=49 }}}

{{{q=49-2 }}}

{{{q=47 }}}



check:

{{{sqrt(47+2)=7 }}}

{{{sqrt(49)=7 }}}

{{{7=7 }}}



b)

{{{sqrt(5-x)=x+1}}}......square both sides

{{{(sqrt(5-x))^2=(x+1)^2}}}

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

{{{0=x^2+2x+x+1-5}}}

{{{x^2+3x-4=0}}}..factor

{{{x^2-x+4x-4=0}}}

{{{(x^2-x)+(4x-4)=0}}}

{{{x(x-1)+4(x-1)=0}}}

{{{(x+4)(x-1)=0}}}

solutions:

{{{(x+4)=0}}}->{{{x=-4}}}


{{{(x-1)=0}}}->{{{x=1}}}


check:

{{{sqrt(5-x)=x+1}}} ->{{{x=-4}}}

{{{sqrt(5-(-4))=-4+1}}}

{{{sqrt(5+4)=-3}}}

{{{sqrt(9)=-3}}}

±{{{3=-3}}}

=>{{{-3=-3}}}


{{{sqrt(5-x)=x+1}}} ->{{{x=1}}}

{{{sqrt(5-1)=1+1}}} 

{{{sqrt(4)=2}}} 

{{{2=2}}}