a. The solution of the equation x + 2 = √3x + 10 is x = -3 or x =2.
b. Extraneous solution is x= -3.
c. Extraneous solution does not satisfy original equation.
As given in the question,
Given equation :
x + 2 = √3x + 10
a. Squaring both the sides
( x + 2 )² = ( √3x + 10 )²
⇒ x² + 4x + 4 = 3x + 10
⇒ x² + x - 6 =0
⇒ x² + 3x -2x -6 =0
⇒ ( x+ 3) ( x -2) =0
⇒ x= -3 or x = 2
b. Extraneous solution:
x = -3
-3 + 2 = √3(-3)+ 10
⇒ -1 ≠ 1 extraneous solution.
x= 2
2+ 2 =√3(2) +10
⇒4 = 4 not extraneous.
c. Extraneous solution does not satisfy original equation
Therefore, the solution of the equation is x = -3 or x=2and its extraneous solution is x =-3. Extraneous solution does not satisfy original equation.
The complete question is :
Use the equation below to answer these questions.
x + 2 = √3x + 10
a) What is the solution to the equation?
b) What is the extraneous solution? Why?
c) In general, what is an extraneous solution?
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