Question

Solve square root of x-9 minus square root of x = -1

Answer 1

\[\sqrt{x-9}-\sqrt{x}=-1\]
\[\sqrt{x-9}\ge0,x \ge9\]
put \[\sqrt{x-9}=a,\sqrt{x}=b,a-b=-1\]
\[a^2-b^2=x-9-x=-9\]
\[\frac{ a^2-b^2 }{ a-b }=\frac{ -9 }{ -1 }=9,a+b=9\]
adding
a-b+a+b=-1+9=8
2a=8
a=4
\[\sqrt{x-9}=4,squaring,\]
x-9=16
x=16+9=25

Answer 2

Thanks

Answer 3

yw