Question

The product of four consecutive natural numbers is 840.Find the numbers.

who will give right answer first
I will mark them as brainlist answer.

don't spam ​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume the four consecutive natural number as

$\begin{gathered}\begin{gathered}\bf\: \begin{cases} &\sf{First \: number \: = \: x} \\ \\ &\sf{Second \: number \: = \: x + 1} \\ \\ &\sf{Third \: number \: = \: x + 2}\\ \\ &\sf{Fourth \: number \: = \: x + 3} \end{cases}\end{gathered}\end{gathered}$

According to statement,

The product of four consecutive natural numbers is 840.

So,

$\rm \: x(x + 1)(x + 2)(x + 3) = 840$

can be rewritten as

$\rm \: x(x + 1)(x + 2)(x + 3) =4 \times 5 \times 6 \times 7$

can be further rewritten as

$\rm \: x(x + 1)(x + 2)(x + 3) =4(4 + 1)(4 + 2)(4 + 3)$

So, on comparing,

$\rm\implies \:\boxed{ \rm{ \:x \: = \: 4 \: }}$

So, four consecutive natural numbers are as follow :

$\begin{gathered}\begin{gathered}\bf\: \begin{cases} &\sf{First \: number \: = \: x = 4} \\ \\ &\sf{Second \: number \: = \: x + 1 = 4 + 1 = 5} \\ \\ &\sf{Third \: number \: = \: x + 2 = 4 + 2 = 6}\\ \\ &\sf{Fourth \: number \: = \: x + 3 = 4 + 3 = 7} \end{cases}\end{gathered}\end{gathered}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Upper Attachments Answer will be given