I do not knw how to proceed further. please help by giving a detailed solution.My attempt
[math]4x⁵-7=A² 4x¹³-7=B²[/math]Subtracting both
[math]B²-A²=4x⁵(x⁸-1)[/math][math](B+A)(B-A)=4x⁵(x⁸-1)[/math][math]B+A=4X⁵[/math][math]B-A=x⁸-1[/math][math]therefore, 2B=X⁸+4X⁵-1[/math]
Note that B+A=4x⁵ and B−A=x⁸−1 is not the only way to factor [imath]4x^5(x^8-1)[/imath].My attempt
[math]4x⁵-7=A² 4x¹³-7=B²[/math]Subtracting both
[math]B²-A²=4x⁵(x⁸-1)[/math][math](B+A)(B-A)=4x⁵(x⁸-1)[/math][math]B+A=4X⁵[/math][math]B-A=x⁸-1[/math][math]therefore, 2B=X⁸+4X⁵-1[/math]
yeah it's certainly not easy..btw answer is x=2..I hope that would help you to figure out more about your approach..if u are able to crack the solution do share it.Note that B+A=4x⁵ and B−A=x⁸−1 is not the only way to factor [imath]4x^5(x^8-1)[/imath].
My quick and dirty script found one solution, but I don't know how to prove that it is the only one. This problem does not look easy to me.
Yeah, I got x=2 too. But no theoriesyeah it's certainly not easy..btw answer is x=2..I hope that would help you to figure out more about your approach..if u are able to crack the solution do share it.
ohh..so were you doing hit and trial?Yeah, I got x=2 too. But no theories