1.

The product of a number and the number 8 more than it is 105.a. What is the least number to be added to make the product a perfect square?b. What are the numbers in the problem?

Answer»

a. Let the number be x, then second number is x + 8

x(x + 8) = 105

x2 + 8x = 105

The number to be added to get a perfect square is 16

b. x2 + 8x + 16 = 121

(x + 4)2 = 121 ;

x + 4 = 11 or -11

x = 7 or -15

number 7, 15 or -15, -7



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