You cannot install an x64 (64-bit) operating system on an x86 (32-bit) processor, not even the new Win 10 or older Windows systems.
That wouldn't make any sense either. This applies to Windows 10 x64 and also for 8.1 x64 and for the new Windows 11.0 and Seven.
The basic requirement for a 64-bit operating system is the possibility of memory addressing using 64-bit. For the 64-bit, for example, Intel Itanium IA64 and EM64T (Extended Memory 64 Technology) are used, and AMD uses the x64 processors (Extended Technology processors).
32Bit (x32 / x86) can be run on x64, the x64 is a 32Bit (x86 / x32) CPU with a 64-bit mode. You can also, for example, install Windows 7 x64 and x86 in parallel on a PC (computer) if the PC is an x64 computer! But you cannot, for example, install Windows 7 x64 on 32bit (x86) computers!
The terms 32-bit and 64-bit refer to the way a computer processor (also known as a CPU) handles information. The benefits of using a 64-bit operating system are most apparent when your computer has a large amount of random access memory (RAM) installed, typically 4 GB of RAM or more. The 64-bit version of Windows handles larger amounts of memory (RAM) more effectively than a 32-bit system. To run a 64-bit version of Windows, your computer must have a 64-bit capable processor.