algebra 2 high school

Question

2 - 3^6 √x=11

solve for all real values of x. Check for extraneous solutions

Answer 1

2-3⁶√x=11

note that 3 is being raised to the sixth power and not -3

2-729√x=11

-729√x=11-2

-729√x=9

√x=9/(-729)

√x=-1/81

√x denotes the principal square root of x; therefore √x must be positive or zero, not negative

there is no solution in the set of real numbers (x=1/6561 is not a solution because √(1/6561)≠(-1/81)