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