Question

the difference of two natural numbers is 7 and their product is 450. find the numbers​

Answer 1

$Let \: x \: and \: y \: are \: two \: natural \\ numbers. ( x > y )$

/* According to the problem given */

$x - y = 7 \: ( given )$

$\implies x = 7 + y \: ---(1)$

$and \: xy = 450 \: (given)$

$\implies (7 + y) y = 450 \: [From \: (1) ]$

$\implies 7y + y^{2} - 450 = 0$

$\implies y^{2} + 7y - 450 = 0$

/* Splitting the middle term,we get */

$\implies y^{2} + 25y - 18y - 450 = 0$

$\implies y( y + 25 ) - 18( y + 25) = 0$

$\implies ( y + 25 )( y - 18 ) = 0$

$\implies y + 25 = 0 \times y - 18 = 0$

$\implies y = - 25 \times y = 18$

$y \: is \: a \: natural \:number . So, y = 18$

/* Substitute y = 18 in equation (1), we get */

$x = 7 + 18$

$\implies x = 25$

Therefore.,

$\red { Required \: two \: natural \: numbers \:are }$

$\green { \: 25 \: and \:18 }$

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Answer 2

The value of two positive no. is 18 and 25