# The product of 4 consecutive numbers which are multiples of 5. is 15,000. Find the natural nos.

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by Charizard

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by Charizard

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It is

5 multiplied by 10 multiplied by 15 multiplied by 20

5 multiplied by 10 multiplied by 15 multiplied by 20

The Brainliest Answer!

∴ x ( x + 5 ) (x – 5 )( x + 10 ) = 15000

∴ (x2 + 5x) (x2 + 10x – 5x – 50) = 15000

∴ (x2 + 5x) (x2 + 5x – 50) = 15000

Put, x2 + 5x = m

∴ m ( m – 50 ) = 15000

∴ m2 – 50 m = 15000

∴ m2 – 50m – 15000 = 0

m2 – 150m + 100m – 15000 = 0

∴ m (m – 150) + 100 (m – 150) = 0

∴ (m – 150) ( m + 100) = 0

∴ m – 150 = 0 OR m + 100 = 0

∴ m = 150 OR m = - 100

∵ Natural Numbers can't be negative,

∴ m ≠ - 100 But m = 150

Now re – substituting,

m = x2 + 5x

m = 150∴ x2 + 5x = 150∴ x2 + 5x – 150 = 0∴ x2 +15x – 10x – 150 = 0∴ x(x + 15 ) – 10 (x + 15) = 0∴ (x + 15) (x – 10) = 0∴ x + 15 = 0 OR x – 10 = 0∴ x = -15 OR x = 10

∵ Natural Number can't be negative∴ x ≠ - 15 But x = 10

∴ x – 5 = 10 – 5 = 5∴ x = 10∴ x + 5 = 10 + 5 = 15∴ x + 10 = 10 + 10 = 20