the sum of the squares of 3 consecutive odd numbers is 83 find the number
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let the first no be x so the other two will be x+1,x+2
x^2+(x+1)^2+(x+2)^2=83
quadratic equation would be formed do it by iddle term splitting....
sorry i cant do it now
x^2+(x+1)^2+(x+2)^2=83
quadratic equation would be formed do it by iddle term splitting....
sorry i cant do it now
Answered by
1
Answer:
Step-by-step explanation:
Given the sum of the squares of 3 consecutive odd numbers is 83
We have to find out the numbers
Let the first number be 'x' , Second number be '(x+2)²'
And third number be '(x+4)²'
We know that,
(x+2)² = x² + 4x + 4
(x+4)² = x² + 8x + 16
x² + x² + 4x + 4 + x² + 8x + 16 = 83
3x² + 12x + 20 = 83
3x² + 12x - 63 = 0
3( x² + 4x - 21 ) = 0
x² + 4x - 21 = 0
Solve this quadratic equation
=
=
=
=
=
=
⇒ x = 3
Hence the numbers are 3 , 5 , 7
3² + 5² + 7² = 9 + 25 + 49 = 83
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