Question

Solve. check for extraneous roots

3^2x+3^x-21

Answer 1

Let
u=3^x, then
u^2=3^(2x)

and substituting into the given equation,
3^(2x)+3^x-21=0
becomes
u^2+u-21=0
=>
u={ -(1/2) + sqrt(85)/2, -1/2-sqrt(85)/2}
={-5.110, 4.110} approximately

To find the value of x, we solve for
3^x=u={-5.110, 4.110}

Since 3^x >0 ∀ x∈R, we see that u=-5.110 is an extraneous root.
Proceeding to solve for x in
3^x=4.110
=> x=1.2865 (approx.)

Answer 2

the answer is 0 hopefully that helps