The sum of two consecutive numbers is 61. What are the numbers?

1.	The sum of two consecutive numbers is 61. What are the numbers?
Answer» Step-by-step explanation: We are given that the SUM of the squares of two consecutive NUMBERS is EQUAL to 61. Let the numbers be x and x+1. So x^2 + (x+1)^2 = 61 => x^2 + x^2 + 1 + 2x = 61 => 2x^2 + 2x - 60 = 0 => x^2 + x - 30 =0 => x^2 + 6x - 5x - 30 =0 => x(x+6) -5(x+6) =0 =>(x-5)*(x+6) =0 We can have x = 5 and x = -6 Therefore the numbers can be 5 and 6 or -6 and -5. The required result is (5, 6) and (-6,-5).

Answer»

Step-by-step explanation:

We are given that the SUM of the squares of two consecutive NUMBERS is EQUAL to 61. Let the numbers be x and x+1.

So x^2 + (x+1)^2 = 61

=> x^2 + x^2 + 1 + 2x = 61

=> 2x^2 + 2x - 60 = 0

=> x^2 + x - 30 =0

=> x^2 + 6x - 5x - 30 =0

=> x(x+6) -5(x+6) =0

=>(x-5)*(x+6) =0

We can have x = 5 and x = -6

Therefore the numbers can be 5 and 6 or -6 and -5.

The required result is (5, 6) and (-6,-5).

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