Question

Two numbers are differ by 3 and their product is 504 .then find number

Answer 1

x-y=3
XY=504
LCM of 504
2³×3²×7
24-21=3 (2³×3-3×7)
x= 24,y=21
the two number are 24&21

Answer 2

Question :-

• Two natural number differ by 3 and their product is 504. Find the numbers.

Solution :-

Let the required numbers be x and

According to the question :

$\implies \: x + (x + 3)=504 \\ </p><p>\implies x {}^{2} + 3x = 504 \\ \implies {x}^{2} + 3x - 504 = 0 \\ \implies x{}^{2} + (24 - 21)x - 504 = 0 \\ \implies \: x {}^{2} + 24x - 21x - 504 = 0 \\ \implies \: x(x + 24) - 21(x + 24) = 0 \\ \implies \: ( x + 24)(x - 21) = 0 \\ \implies \: (x + 24) = 0 \: \: or \: \: (x - 21) = 0 \\ \implies \: x = - 24 \: \: or \: \: x = 21\\\\</p><p>\implies If \:x = - 24, the\:numbers\: are, - 24 \:and\: - 21\\\\</p><p>\implies If \:x = 21, the\: numbers \:are, 21\: and \:24\\\\</p><p>\implies Hence, \:the \:numbers\: are [ -24,-21] \:and \:[ 21,24].$