<input type="text" id="mytext">
<br>
<input type="text" id="mytext2">
<br>
<input type="text" id="mytext3">
<br>

<input type="button" onclick="palindrom()" value="генерировать">

<script>
function palindrom(){

var alphabet = "абвгдеёжзийклмнопрстуфхцчшщъыьэюя";
let palindrom = "";

for (let i = 0; i < 10;i++){
var randomIndex = Math.floor(Math.random() * alphabet.length);
var randomLetter = alphabet[randomIndex];
palindrom = palindrom + randomLetter;
}
document.getElementById("mytext").value = palindrom;

let inversionpalindrom = palindrom.split("").reverse().join("");

document.getElementById("mytext2").value = inversionpalindrom;

palindrom =  palindrom + inversionpalindrom;

document.getElementById("mytext3").value = palindrom;

}
</script>