the sum of the squares of two consecutive odd number is 290 find the number
Answers
Answer:
let the unknown number be x
as both numbers are consecutive odd numbers
the other number will be (x+2)
as every consecutive odd number difer by 2.
given sum of squares is 290.
that is
x² + (x+2)² = 290
x² + x² + 4x + 2² = 290
2x² +4x + 4 = 290
2 ( x² + 2x + 2 ) = 290
x² + 2x + 2 = 290/2
x² + 2x + 2 = 145
x² + 2x + 2 - 145 = 0
x² + 2x - 143 = 0
x² - 11x + 13x - 143 = 0
x ( x - 11 ) + 13 ( x - 11) = 0
(x + 13) (x - 11) = 0
x+13 = 0 or x-11 = 0
x = -13 or x = 11
x = -13 or 11
if we take the value x = (-13)
the other number = -13 + 2 = -11
if we take x = 11
similarly the other number will be x+2 = 11+2 = 13
so the pair of odd numbers required will be (11 and 13) or (-11 and -13)
as both answers satisfies the question
Answer:
The numbers are 11 and 13
Let one number be x
Other number is x+2
(x)^2 + (x+2)^2 = 290
x^2 + x^2 + 4x + 4 = 290
2x^2 + 4x - 286 = 0
Dividing both sides by 2
x^2 + 2x - 143 = 0
By middle term splitting
x^2 + 13x - 11x - 143 = 0 ( 2x = 13x-11x)
x(x+13) - 11( x+13) = 0
(x-11)(x+13) = 0
x-11 = 0
x = 11
Putting the values
x^2 + x^2 + 4x + 4 = 290
11^2 + 11^2 + 4*11 + 4 = 290
121 + 121+ 44 + 4 = 290
290 = 290
So, numbers are 11 and 11 + 2= 13
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