Question

Find the two positive numbers whose sum and product is 5 and 6 respectively

Answer 1

Let the two numbers be x and y.

Given,

x + y = 5

y = 5 - x __(i)

Also,

x × y = 6

Putting value of y in above equation;

x ( 5 - x ) = 6

5x - x² =  6

x² - 5x + 6 = 0

x² - 2x - 3x + 6 = 0

x (x - 2) - 3(x - 2) = 0

x = 2 or x = 3

Putting value in (i);

y = 5 - 2  or  y = 5 - 3

y = 3  or  y = 2

Hence, the two numbers are 2 and 3.

Answer 2

Answer:

2,3

Step-by-step explanation:

Let the two required numbers by a and b

given , sum of numbers = a + b = 5------(1)

product of number = ab = 6 => b = 6/a

put b = 6/a in equation (1)

a + 6/a = 5

${a}^{2} - 5a + 6 = 0 \\ a = 2 \: or \: a = 3$

therefore the numbers are 2 and 3

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