1. Find the largest two digit number whose sum of squares of its digits is 58 and sum of its digits is 10?
Solution:If the number is 10a + b then a + b = 10 and a^2 + b^2 = 58. Solving these equations we get a = 3, b = 7 or a = 7, b = 3. Since we require largest number a = 7 and b = 3 giving 73.
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