Question

What is the solution of the equation sqrt b-17 + sqrt b=1?

Answer 1

Answer:

no solution.

Step-by-step explanation:

The given equation is

$\sqrt{b-17}+\sqrt{b}=1$

$\mathrm{Subtract\:}\sqrt{b}\mathrm{\:from\:both\:sides}\\\sqrt{b-17}+\sqrt{b}-\sqrt{b}=1-\sqrt{b}$

On simplifying, we get

$\sqrt{b-17}=1-\sqrt{b}$

Squaring both sides

$\left(\sqrt{b-17}\right)^2=\left(1-\sqrt{b}\right)^2\\\\b-17=1-2\sqrt{b}+b$

Subtract b from both sides

$17=1-2\sqrt{b}$

On simplifying, we get

$-18=-2\sqrt{b}$

Squaring both sides

$324=4b\\\\b=81$

Now, we substitute this value in the original equation

$\sqrt{81-17}+\sqrt{81}=1\\\\\sqrt{64}+9=1\\\\8+9=1\\\\17=1\text{ This is False}$

Hence, b = 81 is an extraneous solution.

Therefore, the given equation has no solution.