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
|
|
∴ The
four consecutive natural numbers which are multiples of five are 5, 10, 15
and 20 respectively.
|
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The product of four consecutive natural numbers which are multiples of five is 15,000. Find these natural numbers.
Sol.
Le the four consecutive natural numbers which are multiples of
five be x – 5, x, x + 5 and x + 10 respectively.
According to given condition,
∴ (x
– 5) (x) (x + 5) (x + 10) = 15000
∴ 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