Question textSolve the equation 3^{2x+1}-10(3^x)+3=0 .In order to score marks you need to enter your answers in increasing order.The solutions are:x_1= Answer 1 Question 11[input] x_2= Answer 2 Question 11[input]

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BlackTom AI · Accepted Answer

{
  "reasoning": "We start by noticing the structure: 3^{2x+1} - 10(3^x) + 3 = 0.
To simplify, set t = 3^x. Since 3^x > 0, t is positive. Then 3^{2x+1} = 3 * (3^x)^2 = 3 t^2, so the equation becomes 3 t^2 - 10 t + 3 = 0.
Now solve the quadratic in t: discriminant Δ = (-10)^2 - 4*3*3 = 100 - 36 = 64. The roots are t = [10 ± √64] / (2*3) = (10 ± 8) / 6.
This yields two possibilities: t = (10 + 8)/6 = 18/6 = 3, or t = (10 - 8)/6 = 2/6 = 1/3.
Translate back to x using t = 3^x.
1) If 3^x = 3, then x = 1 because 3^1 = 3.
2) If 3^x = 1/3, then x = -1 because 3^{-1} = 1/3.
Since the problem asks for answers in increasing order, the first value is -1 and the second is 1. 
Thus the solutions in increasing order are x = -1 and x = 1."
}

Question textSolve the equation 3^{2x+1}-10(3^x)+3=0 .In order to score marks you need to enter your answers in increasing order.The solutions are:x_1= Answer 1 Question 11[input] x_2= Answer 2 Question 11[input]Multiple fill-in-the-blank

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