Question

find three consecutive odd positive integer the sum of whose square is 371​

Answer 1

Let the odd no be x
Consecutive no will be x ,x+2,x+4
X^2 +(x+2)^2 +(x+4)^2 =371
X^2 + x^2 +4 +4x +x^2 +16+8x=371
3x^2 +12X +20=371
3x^2 +12X =371-20
3x^2 +12X =351
Taking 3 common
X^2 +4X -117
Values of x are 9 and -13
But we need positive integer so we will ignore -13
The final concepito è numbers are
9,11,13

Answer 2

Answer:

The consecutive odd no.s are 9, 11, 13.

Step-by-step explanation:

Let the no.s be 2k + 1, 2k + 3, 2k + 5

==> (2k + 1)² + (2k + 3)² + (2k + 5)² = 371

==> 4k² + 4k + 1 + 4k² + 12k + 9 + 4k² + 20k + 25 = 371

==> 12k² + 36k + 35 = 371

==> 12k(k + 3) = 336

==> k(k+3) = 28

==> k² + 3k = 28

∴ k = 4

∴ 2k + 1 = 2 × 4 + 1 = 9

∴ 2k + 3 = 2 × 4 + 3 = 11

∴ 2k + 5 = 2 × 4 + 5 = 13

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