Question

If the sum of two nembers is 13 and their product is 42. determine.

Answer 1

Answer:

Suppose the two numbers be a and b

(a + b) = 13

ab = 42

so that, it requires formula theory-

................

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

Numbers be x and y (y < x)

Given,

${\boxed{\sf\:{Sum\;of\;Number}}}$

= x + y = 13

${\boxed{\sf\:{Product\;of\;Number}}}$

xy = 42

Hence now,

x + y = 13

x = 13 - y ............. (1)

xy = 42

${\boxed{\sf\:{Putting\;value\;in\;(1)}}}$

(13 - y)y = 42

13y - y² = 42

y² - 13y + 42 = 0

y² - (7 + 6)y + 42 = 0

y² - 7y - 6y + 42 = 0

y(y - 7) - 6(y - 7) = 0

(y - 7)(y - 6) = 0

Therefore,

If y - 6 = 0

y = 6

Also,

x = 13 - y

x = 13 - 6

x = 7

If y - 7 = 0

y = 7

x = 13 - y

x = 13 - 7

x = 6

Hence,

$\Large{\boxed{\sf\:{Required\;number = 6\;and\;7}}}$