Germany| A Math Olympiad algebraic question.

A math Olympiad question was solved using the knowledge of polynomials. #matholympiad #algebraproblems

[petruscerisier]

8^x+ 2^x=130
(2³)^x + 2^x -130=0
Let y=2^x
y³ + y - 130 =0
y= 26y - 25y and 130= 26*5
=> y³ -25y + 26y - 5*26=0
y(y² -25) + 26(y-5)=0
a² - b²= (a+b)(a-b)
y(y+5)(y-5) + 26(y-5)=0
(y-5)(y²+5y+26)=0
y-5=0
y=5

[RyanLewis-Johnson-wqxs]

8^(Log[2, 1.25]+2)+2^(Log[2, 1.25]+2)=130 x=Log[2, 5]=Log[2, 125]+2 It’s in my head.