Kayla's school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 6 adult tickets and 14 child tickets for a total of $172. The school took in $142 on the second day by selling 3 adult tickets and 14 child tickets. What is the price of one adult ticket and one child ticket?

The problem is as follow: which of the following is an extraneous solution of √(4x + 41) = x+5 a. x=-8 b. x=-2 c. x=2 d. x=8 solution: √(4x + 41) = x+5squaring both sides∴ 4x +41 = (x+5)²∴ 4x +41 = x² + 10x + 25∴ x² + 6x - 16 = 0∴ ( x + 8)( x - 2) = 0∴ x = -8  or    x = 2by substitution in the given equation: substitute with x = -8left hand side =√(4*-8+41) = √9 right hand side =-8 +5 = -3the basic principal of the square root is to give a positive answer.so, x =-8  ⇒ is not an extraneous solutionsubstitute with x = 2left hand side =√(4*2+41) = √49 right hand side = 2+5 = 7∴ x=2  ⇒ is an extraneous solutionthe correct choice is option  (c)c. x = 2