The sum of the squares of three positive numbers that are consecutive multiples of 5 is 725. Find the three numbers.Spams not allowed ❌
Answers 2
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
[tex] {(5x)}^{2} \\ {(5x + 5)}^{2} \\ and \\ {(5x + 10)}^{2} [/tex]
[tex] {(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 [/tex]
So numbers are 10,15 and 20
Hope it helps you from my side
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Author:
tatianaht9e
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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 (◠‿◕)-
Author:
eliezergj6h
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10
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