Sum of squares of digit is 50 and left digit is greater than right digit. Find…

Answer: 7

Let the left digit be x and the right digit be y. We are given x^2 + y^2 = 50 and x > y.

• Check possible digit squares (0 through 9): 0, 1, 4, 9, 16, 25, 36, 49. The only combinations that sum to 50 are 49 + 1 and 25 + 25.

• 49 + 1 corresponds to digits 7 and 1; 25 + 25 corresponds to digits 5 and 5.

• The pair with equal digits (5 and 5) does not satisfy x > y, so it is not allowed. Therefore the only valid digits are x = 7 and y = 1.

• Compute the product: 7 × 1 = 7. Since this is the only valid pair, 7 is the required (and highest) product.

Final answer: 7