Answer:
no solution.
Step-by-step explanation:
The given equation is
[tex]\sqrt{b-17}+\sqrt{b}=1[/tex]
[tex]\mathrm{Subtract\:}\sqrt{b}\mathrm{\:from\:both\:sides}\\\sqrt{b-17}+\sqrt{b}-\sqrt{b}=1-\sqrt{b}[/tex]
On simplifying, we get
[tex]\sqrt{b-17}=1-\sqrt{b}[/tex]
Squaring both sides
[tex]\left(\sqrt{b-17}\right)^2=\left(1-\sqrt{b}\right)^2\\\\b-17=1-2\sqrt{b}+b[/tex]
Subtract b from both sides
[tex]17=1-2\sqrt{b}[/tex]
On simplifying, we get
[tex]-18=-2\sqrt{b}[/tex]
Squaring both sides
[tex]324=4b\\\\b=81[/tex]
Now, we substitute this value in the original equation
[tex]\sqrt{81-17}+\sqrt{81}=1\\\\\sqrt{64}+9=1\\\\8+9=1\\\\17=1\text{ This is False}[/tex]
Hence, b = 81 is an extraneous solution.
Therefore, the given equation has no solution.
