The product of two consecutive natural number is 31 less than the sum of their squares. Find the numbers
Answers
Answered by
5
let the numbers be n and n+1
n²+(n+1)²-n(n+1)=31
n²+n²+2n+1-n²-n=31
n²+n+1=31
n(n+1)=30
so the number are 5 and 6
because other factors are not consecutive
n²+(n+1)²-n(n+1)=31
n²+n²+2n+1-n²-n=31
n²+n+1=31
n(n+1)=30
so the number are 5 and 6
because other factors are not consecutive
Answered by
18
Hi !
Let the two consecutive natural numbers be "x" and "x + 1"
A.T.Q.,
x² + (x+1)² - 31 = x(x+1)
2x² + 2x + 1 - 31 = x² + x
x² + x - 30 = 0
x² + 6x - 5x - 30 = 0
x( x + 6) - 5 ( x + 6) = 0
( x - 5) ( x + 6) = 0
x = -6 , x = 5
The positive value of x is taken , as it is a natural no:,
x = 5
x + 1 = 6
the no:s are 5 and 6.
Let the two consecutive natural numbers be "x" and "x + 1"
A.T.Q.,
x² + (x+1)² - 31 = x(x+1)
2x² + 2x + 1 - 31 = x² + x
x² + x - 30 = 0
x² + 6x - 5x - 30 = 0
x( x + 6) - 5 ( x + 6) = 0
( x - 5) ( x + 6) = 0
x = -6 , x = 5
The positive value of x is taken , as it is a natural no:,
x = 5
x + 1 = 6
the no:s are 5 and 6.
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