Question

2 numbers whose sum is -11 and product is 24

Answer 1

Answer:

Let one number be x.

Then another number = 24-x

P=x(24−x)

P=24x−x2

P′(x)=24−2x

P′′(x)=−2

Now, P′(x)=0⟹x=12

Also, P′′(12)=−2<0 (maxima)

Hence, the product of the numbers is maximum when the numbers are 12 and 12.

Answer 2

Answer:

let the two numbers =x and y

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

y=-11-x

xy=24...........(2)

put value of y in equation 2

x(-11-x)=24

-11x-x^2=24

x^2+11x+24=0

x^2+3x+8x+24= 0

x(x+3) +8(x+3) =0

x+3=0 x+8=0

x=-3 x=-8

put values of x in equation 1

-3+y = -11 -8+y=-11

y= -11+3 y=-3

y=-8