Question

the sum of the ages of two friend is 20. four years ago, the product of their age in years was 48. is it possible to determine their present age

Answer 1

Answer:

Step-by-step explanation:

let the ages be x and y

x+y=20---------------(1)

4 years ago......

(x-4)(y-4)=48

xy-4x-4y-16=48

xy-4(x+y)=48+16

xy-4(20)=64

xy=144

x=144/y

substitute in (1)

x+y=20

144/y+y=20

144+y²=20y

y²-20y+144=0

which is impossible to be solved

so, it is impossible

Answer 2

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

★Assumption

★Age of 1 friend = n years

★Age of other friend = 20 - c

★4 years ago,

${\boxed{\sf\:{Age\;of\;1\;friend}}}$

= (n - 4)

${\boxed{\sf\:{Age\;of\;other\;friend}}}$

= (20 - n - 4)

= (16 - n)

$\fbox{Situation\;should\;be\;like\;that :-}$

(n - 4)(16 - n) = 48

16n - n² - 64 + 4n = 48

n² - 20n + 112 = 0

★Now :-

${\boxed{\sf\:{Using\;the\;formula :-}}}$

a = 1

b = -20

c = 112

★D = b² - 4ac

D = (-20)² - 4(1)(112)

D = 400 - 448

D = -48

★Therefore,

$\fbox{Equation\;has\;No\;real\;roots}$

$\fbox{Situation\;is\;not\;possible}$