A full video on math Olympiad exponential question. #maths #matholympiad #algebra I upload videos twice daily. Please always tune in to check for new uploads.
Thank you for explaining. I would like to show the 2 points as follows: 1) There is another solution: x = -(4^(1/10)) [ There are 2 real solutions. ] 2) As for writing the final answer, 2^(1/5) is better than 4^(1/10) . Therefore, my final answer is x = ± 2^(1/5) . >
Break 80 to 64 + 16 i.e. 4^3 + 4^2. No ned to waste time in trial and error. This will become t^3 - 4^3 + t^2 -4^2 = 0 then it will factor out to (t - 4){(t^2 + 4t + 16) + (t + 4)} =0 which implies (t-4){t^2 + 5t + 20) = 0. From here you can find t = 4 and solve the quadratic equation.
This problem has 30 roots. Substitute y=x^10 into the given equation: y^3+y^2-80=0. By inspection y=4. Divide by (y-4): y^2+5y+20=0 with roots y=(-5±i√55)/2. Ten 10th roots of 4, (-5+i√55)/2, and (-5-i√55)/2.
