A awesome mathematics exponential & radical problem | Olympiad Question | x=?

[@HuzaifaKhan-m3i]

❤❤❤❤❤

[@HuzaifaKhan-m3i]

Great question sir g ❤❤❤❤

[@Ismailorakzai-u1m]

Amazing❤❤❤

[@SrisailamNavuluri]

Here x is even multiple . Let x=2y 4,(388-4y^2)=4×4(97-y^2)=2^4(97-y^2) 97=81+16=3^4+2^4 97-16=3^4 or 97--81=2^4 So y^2=81 or 16 Y=9 or 4 x=2×9 or 2×4=18 or 8 so that √2x=√36 or √16 x=18 or 8 x=18 {4(388-324)}^1/4+√2×18=(4×64)^1/4+√36 =4+6=10 2nd case:x=8 {4(388-64)}^1/4+√2×8 ={4×18×18}^1/4+4=6+4=10

[@gregevgeni1864]

Let p = ⁴√(4(388-x²)) and q = √(2x) => p⁴=4•(388-x²) (1) and q² =2x => 4x² = q⁴ (2) with x ≥ 0. From the original equation and (1) and (2) => p +q = 10 and p⁴+ q⁴ =4•388 . Solving the system of the last equations we have (p,q)=(4,6) or (p,q)=(6,4) .. For p=4 or p= 6 => x=8 or x=18. Recall x≥0 => both of the solutions x=8, x=18 are accepted ..