1.

The sum of a number and its square is 63/4, find the numbers.

Answer»

Let the number be ‘a’ 

⇒ a + a2 = 63/4 

⇒ 4a2 + 4a – 63 = 0 

⇒ 4a2 + 18a – 14a – 63 = 0 

⇒ 2a(2a + 9) – 7(2a + 9) = 0 

⇒ (2a – 7)(2a + 9) = 0 

⇒ a = 7/2 or – 9/2



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