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Let the smaller number be 'a' and larger number be 'b'. a + b = 20 -------- (I) And, a2 = 5b + 4 Or, a2 = 5 X (20 - a) + 4 (from equation I) Or, a2 = 100 - 5a + 4 Or, a2 + 5a - 104 = 0 Or, a2 + 13a - 8a - 104 = 0 Or, a(a + 13) - 8(a + 13) = 0 Or, (a - 8) (a + 13) = 0 So, 'a' = 8 or 'a' = - 13 But given that both are natural numbers, So, 'a' = 8 On putting value of 'a' in equation I, We get, 'b' = 20 - 8 = 12 Therefore, required product = 12 X 8 = 96
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