Question

The difference between two numbers is2 and their product is 1443. Find the number by linear equations in two variables

Answer 1

let the number be x and y
$x - y = 2 \\ xy = 1443 \\ x = \frac{1443}{y} \\ \frac{1443}{y} - y = 2 \\ 1443 - {y}^{2} = 2y \\ - {y}^{2} - 2y + 1443 = 0 \\ {y}^{2} + 2y -1443 = 0 \\ {y}^{2} + 39x - 37x - 1443 = 0 \\ y(y + 39) - 37(y + 39) = 0 \\ (y - 37)(y + 39) = 0 \\ y = 37 \: \: \: \: \: and \: \: \: \: y = - 39(neglect \: negative \: value \: if \: want \\ x - 37 = 2 \\ x = 39 \\ so \: the \: numbers \: are \: 39 \: and \: 37$

Answer 2

Hey friend!

Here is your answer!
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Let the numbers be x and y
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According to question :

x-y=2

So, x=y+2 -------------------------(i)

xy=1443 -------------------------(ii)
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Putting x=y+2 from eq(i) in eq(ii)

We get,

(y+2)y=1443

y²+2y=1443

y²+2y-1443=0

y²+39y-37y-1443=0

y(y+39)-37(y+39)=0

(y+39)(y-37)=0

y= -39 or y=37
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When y= -39

x=y+2

x= -39+2

x= -37

When y=37

x=y+2

x=37+2

x=39
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So the numbers are -37 and -39 or 39 and 37
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Hope it's satisfactory!