Question
If the product of two numbers is 60 and the sum of
their squares is 169, then what is the sum of these two numbers?Solution
Let the two numbers be x and y Then, ATQ: xy = 60    ----eq.(1) x2+ y2 = 169    ----eq.(2) Also, (x + y)2 = x2 + y2 + 2xy ⇒ (x + y)2 = 169 + (2 × 60); From eq.1 and eq.2 ⇒ (x + y)2 = 289 ⇒ x + y = 17 ∴ Sum of the two numbers = 17
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