The Sum of the Squares of three Positive Numbers that are Consecutive Multiples of 5 is 725. Find the Three Numbers | Bzziii.com

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




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

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

⇒ `(5"x")^2` + `(5"x" + 5)^2` + `(5"x" + 10)^2` = 725 

⇒ `25"x"^2` + `25"x"^2` + 50x + 25 + `25"x"^2` + 100x + 100 = 725

⇒ `75"x"^2` + 150x - 600 = 0

⇒ `"x"^2` + 2x - 8 = 0

⇒ (x + 4) (x - 2) = 0

∴ x + 4 = 0 and x - 2 = 0

⇒ x + 4 = 0

⇒ x = -4 		⇒ x - 2 = 0

⇒ x = 2
∴ x =-4 and 2  

Hence, Ignoring the negative value of x that is -4. So the Value of x is 2.

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

By Putting x's  Value on three consecutive multiples 

⇒ 5x, 5x + 5, 5x + 10

⇒ (5`\times`2), (5`\times`2 + 5) and (5`\times`2 + 10) 

⇒ 10, 15 and 20

So, the three consecutive multiples are 10, 15 and 20






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