Math

QuestionIf n=1n=1 is a solution to n+2=ann + 2 = \sqrt{a - n}, what is the value of the constant aa?

Studdy Solution

STEP 1

Assumptions1. The given equation is n+=ann + = \sqrt{a - n} . n=1n =1 is a solution to the equation3. aa is a constant

STEP 2

First, we need to substitute n=1n =1 into the equation to find the value of aa.
1+2=a11 +2 = \sqrt{a -1}

STEP 3

implify the left side of the equation.
3=a13 = \sqrt{a -1}

STEP 4

To isolate aa, we need to square both sides of the equation.
(3)2=(a1)2(3)^2 = (\sqrt{a -1})^2

STEP 5

Calculate the square of both sides.
9=a19 = a -1

STEP 6

Finally, solve for aa by adding1 to both sides of the equation.
a=9+1a =9 +1

STEP 7

Calculate the value of aa.
a=10a =10So, the value of aa is10 when n=1n =1 is a solution to the equation.

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