the sum of two consecutive numbers is 61 .what are the number in algebraic equations
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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.
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