Interesting Radicals

[@swarnendukarfa8480]

Let √x = a a² - ⁶⁄ₐ = 37 Multiplying both sides by a², a⁴ - 6a = 37a² or, a⁴ - a² - 6a = 36a² or, a⁴ - 36a² = a² + 6a or, (a² - 6a)(a² + 6a) = a² + 6a ∴ a² - 6a = 1 [ ∵ a ≠ 0] or, x - 6√x = 1

[@mcwulf25]

Good methods 👍 I thought that 37=36+1 would come in to it but didn't try to solve it this time 🙃

[@scottleung9587]

Nice!

[@tanseng5867]

From your first method,(t+6)(t^2-6t-1)=0 imply t=6 (rejected) or t^2-6t=1 This is the answer.

[@anshult]

kzbin.infoWfNDs69a41c?si=B38R8tVC1foGhBaV

[@yakupbuyankara5903]

1

[@rakenzarnsworld2]

x is greater than 37 and lesser than 38 Answer: 1

[@giuseppemalaguti435]

1...

[@alexchan4226]

-6，6，-37，37