How do you solve #sqrt(9-b)=sqrt(1-9b)#?

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Answer 1 · 2017-06-12T00:04:46

#b = - 1#

We have: #sqrt(9 - b) = sqrt(1 - 9 b)#

Let's square both sides of the equation:

#Rightarrow (sqrt(9 - b))^(2) = (sqrt(1 - 9 b))^(2)#

#Rightarrow 9 - b = 1 - 9 b#

Then, let's add #9 b# to both sides:

#Rightarrow 9 - b + 9 b = 1 - 9 b + 9 b#

#Rightarrow 9 + 8 b = 1#

Now, let's subtract #9# from both sides:

#Rightarrow 9 + 8 b - 8 = 1 - 9#

#Rightarrow 8 b = - 8#

Finally, to solve for #b#, let's divide both sides by #8#:

#Rightarrow frac(8 b)(8) = - frac(8)(8)#

#therefore b = - 1#

Therefore, the solution to the equation is #b = - 1#.