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प्रश्न
The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers.
उत्तर
Let the numbers be 3x, 3 (x +1)
According to question, (3x) × 3( x + 1) = 810
`9 [ x^2 + x ] =810`
`x^2 + x = 90`
`x^2 + x - 90 = 0 `
`x^2 + 10x -9x - 90 = 0`
x ( x + 10) - 9 ( x +10 ) = 0
(x - 9) (x + 10 ) = 0
x = 9 , x = - 10
But x ≠ - 10, because 3x must be natural number .
∴ x = 9
Numbers are 3x, 3 (x +1 )
⇒ 3 × 9 , 3(9 + 1)
∴ Numbers are ⇒ 27 , 30
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