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irina [24]
3 years ago
13

Quadratic Equation

Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
7 0

Step-by-step explanation:

The sum of ages of two friends is 13 years.

The product of their ages is 42.

<em>Let the age of 1st friend and 2nd friend is x, y respectively.</em>

<em>1 st condition= The sum of ages of two friends is 13 y</em><em>r</em><em>s. </em>

i.e x+y = 13........ (I)

<em>2nd condition= The product of their ages is 42.</em>

i.e X*y = 42........(ii)

From equation (I)

X+y = 13

or, X = 13-y........ (iii)

<em>Putting the equation (iii) in equation (ii).</em>

X*y= 42

(13-y) * y = 42

13y - y^2 = 42

{y}^{2}  - 13y + 42 = 0

{y}^{2}   - (7 + 6)y + 42= 0

{y}^{2}  - 7y - 6y + 42 = 0

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

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

Either; y-6 = 0

y = 6

Or;

y-7=0

y = 7

<em>Keeping the value of y as "7" in equation (ii)</em>

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.

<em><u>H</u></em><em><u>o</u></em><em><u>p</u></em><em><u>e</u></em><em><u> </u></em><em><u>it </u></em><em><u>helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>

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