Question

Find two numbers whose sum is 11 and product is 30

Answer 1

Answer:

Answer is (5,6)

Step-by-step explanation:

Let two numbers are x and y

x + y = 11

xy = 30

x= 30/y

30/y + y = 11

30 + y² = 11y

y²- 11y + 30 = 0

y=5,6

x=6,5

( x , y) = (5 , 6)

Answer 2

Let the two numbers are x and y

According to the question,

x+y = 11......(1)

xy = 30......(2)

From equation no. 1

x+y = 11

--» x = 11-y......(3)

From equation no. 2

xy = 30

--» x = 30/y......(4)

By comparing equation no. 3 and 4 we will get

11-y = 30/y

--» 11y-y² = 30

--» -(30+y²) = -11y

--» 30+y² = 11y

--» 30+y²-11y = 0

--» y²-5y-6y+30 = 0

--»y(y-5)-6(y-5) = 0

--» (y-5)(y-6) = 0

As the rule of quadratic equation we know that if the multiplication of two numbers is zero one of them or two of them would be zero. So, we can write,

Either,

y-5 = 0

--» y = 5

Then,

x+5 = 11 (From equation no. 1)

--» x = 6

Or,

y-6 = 0

--» y = 6

Then,

x+6 = 11

--» x = 5

So, the two numbers are 5 and 6.