Question

a 2 digit number is such that it tens digit is greater than it's units digit by four. the two-digit number is less than four times the product of its digits by 11..find the number

Answer 1

Let \(n=10a+b\), where \(a,b\in\mathbb{Z}\), \(1\leq a\leq 9\), and \(0\leq b\leq 9\).

We know that \(a=b+4\) and that \(n=10a+b=11b+40<44b^2+176b=4\cdot 11\cdot a\,b\).

Answer 2

So \(0<44b^2+165b-40\), which is a simple quadratic...

Answer 3

thanks