Question

The difference of two numbers is 5 the difference of their square is 45 find the numbers

Answer 1

Answer:-

Let the numbers be x and y.

So, according to the given conditions,

$\sf x - y = 5 \: \: ...(i)$

$\sf {x}^{2} - {y}^{2} \: ...(ii)$

Now, dividing equation (ii) by (i), we get,

$\sf \implies \frac{ {x}^{2} - {y}^{2} }{x - y} = \frac{45}{5}$

$\sf \implies \frac{(x + y) \cancel{(x - y) }}{ \cancel{(x - y)}} = 9$

$\sf \implies x + y = 9 \: ...(iii)$

Adding equations (i) and (iii), we get,

$\sf \implies x - y + x + y = 5 + 9$

$\sf \implies 2x = 14$

$\sf \implies x = 7$

Putting the value of x in equation (i), we get,

$\sf \implies 7 - y = 5$

$\sf \implies y = 7 - 5$

$\sf \implies y = 2$

Hence, the numbers are 7 and 2.

Answer 2

Answer:

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