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Step-by-step explanation:
The sum of ages of two friends is 13 years.
The product of their ages is 42.
Let the age of 1st friend and 2nd friend is x, y respectively.
1 st condition= The sum of ages of two friends is 13 yrs.
i.e x+y = 13........ (I)
2nd condition= The product of their ages is 42.
i.e X*y = 42........(ii)
From equation (I)
X+y = 13
or, X = 13-y........ (iii)
Putting the equation (iii) in equation (ii).
X*y= 42
(13-y) * y = 42
13y - y^2 = 42
[tex] {y}^{2} - 13y + 42 = 0[/tex]
[tex] {y}^{2} - (7 + 6)y + 42= 0[/tex]
[tex] {y}^{2} - 7y - 6y + 42 = 0[/tex]
[tex]y(y - 7) - 6(y - 7) = 0[/tex]
[tex](y - 6) (y - 7) = 0[/tex]
Either; y-6 = 0
y = 6
Or;
y-7=0
y = 7
Keeping the value of y as "7" in equation (ii)
x*y = 42
7x = 42
X = 42/7
Therefore, the value of X is 6.
Therefore, either 1st friend is 6 years and 2nd is 7 years.
Hope it helps...