Question

The sum of the squares of five consecutive natural numbers is 1455 find them

Answer 1

$\huge \fbox \red{Answer : 15, 16, 17, 18, and 19}$

Solution :

${x}^{2} + {(x + 1)}^{2} + {(x + 2)}^{2} + {(x + 3)}^{2} + {(x + 4)}^{2} = 1455 \\ \\ = > {x}^{2} + ( {x}^{2} + 2x + 1) + ( {x}^{2} + 4x + 4) + ( {x}^{2} + 6x + 9) + ( {x}^{2} + 8x + 16) = 1455 \\ \\ = > 5 {x}^{2} + 20x + 30 = 1455 \\ \\ = > 5 {x}^{2} + 20x - 1425 = 0 \\ \\ = > {x}^{2} + 4x - 285 = 0 \\ \\ = > {x}^{2} + 19x - 15x - 285 = 0 \\ \\ = > x(x + 19) - 15(x + 19) = 0 \\ \\ = > (x + 19)(x - 15) = 0$

Required values of x : 15 and -19

Since, we can't accept the negative value so the only value of x will be 15

Hence, 5 consecutive numbers will be : 15, 16, 17, 18, and 19 ✔✔

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Hope it helps ☺

Fóllòw Më ❤

Answer 2

Step-by-step explanation:

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