Question

the product of four consecutive natural numbers is 840 find tha number​

Answer 1

The product are 4 consecutive positive no 840 , then the no's are 4,5,6,7

Answer 2

Giνєи —

• The product of four consecutive natural numbers is 840 .

Tσ Fiиd —

• The numbers ?

Cσиcєρт —

• Arithmetic progressions

Sσℓυтiσи –

✪ Let the conductive natural numbers be x , ( x + 1 ) , ( x + 2 ) , ( x + 3 )

Therefore , according to question :

➙ x ( x + 1 ) ( x + 2 ) ( x + 3 ) = 840

➙ x ( x + 3 ) ( x + 1 ) ( x + 2 ) = 840

➙ ( x² + 3x ) [x ( x + 2 ) + 1 ( x + 2 )] = 840

➙ ( x² + 3x ) [x² + 2x + x + 2 = 840

➙ ( x² + 3x ) ( x² + 3x + 2 ) = 840

ㅤ

✪ Let x² + 3x = m

➙ m ( m + 2 ) = 840

➙ m² + 2m = 840

➙ m² + 2m - 840 = 0

➙ m² + 30m - 28 m - 840 = 0

➙ m ( m + 30 ) - 28 ( m + 30 ) = 0

➙ ( m + 30 ) ( m - 28 ) = 0

➙ m + 30 = 0 and m - 28 = 0

➙ m = - 30 and m = 28

➻ We need natural numbers .

m ≠ -30 and m = 28

ㅤ

➙ x² + 3x = 28

➙ x² + 3x - 28 = 0

➙ x² + 7x - 4x - 28 = 0

➙ x ( x + 7 ) -4 ( x + 7 ) = 0

➙ ( x + 7 ) ( x -4 ) = 0

➙ x + 7 = 0 and x - 4 = 0

➙ x = -7 and x = 4

➻ As we need only natural numbers :

x ≠ -7 and x = 4

ㅤ

Tнerefore , the four conductive natural number :

• x = 4
• ( x + 1 ) = 4 + 1 = 5
• ( x + 2 ) = 4 + 2 = 6
• ( x + 3 ) = 4 + 3 = 7

❝ Hence the four consuctive natural numbers are , 4 , 5 , 6 and 7 ❞