Math, asked by riaritushalu, 2 months ago

The product of two consecutive natural numbers which are multiples of 6 is equals to 1080. Find the numbers.​

Answers

Answered by tiwarivivekanand9
3

Step-by-step explanation:

according to the question -

6y ×6(y+1) =1080

=> y(y+1) =1080/36

=> y^2 +y -30=0

=>y^2+6y-5y-30=0

y(y+6) -5(y+6)=0

( y+6) (y-5)=0

y=5and y=-6

Answered by varadad25
19

Answer:

The required numbers are 30 & 36.

Step-by-step-explanation:

Let the first multiple of 6 be 6x.

And the consecutive natural number be 6 ( x + 1 ).

From the given condition,

6x [ 6 ( x + 1 ) ] = 1080

⇒ 6x ( 6x + 6 ) = 1080

⇒ 36x² + 36x - 1080 = 0

⇒ 36 ( x² + x - 30 ) = 0

⇒ x² + x - 30 = 0

⇒ x² + 6x - 5x - 30 = 0

⇒ x ( x + 6 ) - 5 ( x + 6 ) = 0

⇒ ( x + 6 ) ( x - 5 ) = 0

⇒ ( x + 6 ) = 0 OR ( x - 5 ) = 0

⇒ x + 6 = 0 OR x - 5 = 0

x = - 6 OR x = 5

The number is a natural number.

∴ x = - 6 is not acceptable.

x = 5

Now,

First number = 6x = 6 * 5 = 30

Now,

Second consecutive number = 6 ( x + 1 )

⇒ Second consecutive number = 6 ( 5 + 1 )

⇒ Second consecutive number = 6 * 6

Second consecutive number = 36

∴ The required numbers are 30 & 36.

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