The product of digits of a two – digit number is 8 and the sum of the squares of the digits is 20. If the number is less than 25. Find the number.

Question

Philoid · Accepted Answer

The product of digits of a two – digit number is 8

Let digit at tens place be x

Now,given –

⇒ x⁴ + 64 = 20x²

⇒ x⁴ – 20x² + 64 = 0

⇒ x⁴ – (16 + 4)x² + 64 = 0

⇒ x²(x² – 4) – 16(x² – 4) = 0

⇒ (x² – 16) (x² – 4) = 0

⇒ x = 4 or x = 2

For x = 4,

Original no.

= 42

For x = 2,

Original no.

= 24

Given no. is less than 25 –

⇒ two – digit no. = 24