Question

The sum of the squares of three positive numbers that are consecutive multiples of 5 is 725. Find the three numbers.


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Answer 1

Answer:

Hello Santa19!

10,15 and 20 are the three numbers

Step-by-step explanation:

Let the three consecutive multiples of 5 be 5x, 5x + 5, 5x+10

Their square are

${(5x)}^{2} \\ {(5x + 5)}^{2} \\ and \\ {(5x + 10)}^{2}$

${(5x)}^{2} + {(5x + 5)}^{2} + {(5x + 10)}^{2} = 725 \\ \\ = {25x}^{2} + {25x}^{2} + 50x + 25 + {25x}^{2} + 100x \\ + 100 = 725 \\ \\ = {75x}^{2} + 150x - 600 = 0 \\ \\ {x}^{2} + 2x - 8 = 0 \\ \\ = (x + 4)(x - 2) = 0 \\ \\ = x = - 4 \: and \: 2 \\ \\ x = 2$

So numbers are 10,15 and 20

Hope it helps you from my side

Answer 2

Let the three consecutive multiples of 5 be 5x, 5x + 5, 5x + 10.

Their squares are (5x)2, (5x + 5)2 and (5x + 10)2.

(5x)2 + (5x + 5)2 + (5x + 10)2 = 725

⇒ 25x2 + 25x2 + 50x + 25 + 25x2 + 100x + 100 = 725.

75x² + 150x - 600 = 0

x² + 2x - 8 = 0

(x + 4)(x - 2) = 0

x = -4,2

x= 2 (ignoring -ve value)

So the numbers are 10,15 and 20 (◠‿◕)