Question

what is the maximum product of two numbers whose sum is -8

Answer 1

if you let x - 1st number and y - 2nd number, P is the product of two number then \[P=xy~~~~(1)\]\[x+y=-8~~~~(2)\]we can re-write (2) as \[y=-8-x\]and substitute it to (1) \[P=x(-8-x)=-8x-x^2\]re-arranging\[-P=x^2+8x\]

Answer 2

There are two ways we can solve this, either we work on the quadratic part by applying "Completing the square" or apply differential calculus and solve for maximum...

Answer 3

Applying completing the square: \[-P+16=x^2+8x+16\]\[-P+16=\left(x+4\right)^2\]This result means that the maximum product P is 16 from \[-P+16=0\]\[P=16\]One of the number is also known as x=-4 from \[x+4=0\]\[x=-4~~~~the~1st~number\]and so using (2) \[x+y=-8\]\[(-4)+y=-8\]\[y=-8+4\]\[y=-4~~~~the~2nd~number\]

Answer 4

hope i explain it clearly... :)

Answer 5

thank you so much!! you did :)

Answer 6

16