Question

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

b = 3
b = 9
b = 81
no solution

Answer 1

no solution

Explanation:

person above me was right :)

Answer 2

no solution.

Explanation:

The given equation is

`√(b-17)+√(b)=1`

`\mathrm{Subtract\:}√(b)\mathrm{\:from\:both\:sides}\\√(b-17)+√(b)-√(b)=1-√(b)`

On simplifying, we get

`√(b-17)=1-√(b)`

Squaring both sides

`\left(√(b-17)\right)^2=\left(1-√(b)\right)^2\\\\b-17=1-2√(b)+b`

Subtract b from both sides

`17=1-2√(b)`

On simplifying, we get

`-18=-2√(b)`

Squaring both sides

`324=4b\\\\b=81`

Now, we substitute this value in the original equation

`√(81-17)+√(81)=1\\\\√(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.