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