The sum of the squares of three comsecutive natural numbers is 302.what is the middle number
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Answer:
Step-by-step explanation:
Answered by
0
Answer:
x = 9
x= 10
x=11
Step-by-step explanation:
take three consecutive numbers as
x , x+1 , x+2
given that
(x^2) +(x+1)^2 + (x+2)^2 = 302
x^2 + x^2 + 1 + 2x + x^2 + 4x + 4 = 302
add all the like terms
3x^2 + 5 + 6x = 302
3x^2 +6x +5- 302 =0
3x^2 +6x - 297 = 0
divide the equation with 3 to make x square coefficient as 1
x^2 + 2x - 99 = 0
product is -99
sum is 2
factors are 11 and -9
x^2 -9x +11x -99 =0
x( x-9) + 11 ( x-9) =0
(x+11) + ( x -9) = 0
x = -11 or x= 9
as -11 is not a natural number
x = 9
x+1 =10
x+2 =11
the middle number is 10
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