Question

What are two numbers that multiply to 64 and add to - 20

Answer 1

Let they be a and b

• a+b=-20--(1)
• ab=64

So

`\\ \rm\rightarrowtail (a-b)^2=(a+b)^2-4ab`

`\\ \rm\rightarrowtail (a-b)^2=(-20)^2-4(64)=400-256=144`

`\\ \rm\rightarrowtail a-b=12\dots(2)`

From both equations

• 2a=-8=>a=-4
• -4+b=-20
• b=-16

Answer 2

-4 and -16

Explanation:

Let x = first number

Let y = second number

Given:

• The two numbers multiply to 64

⇒ xy = 64

Given:

• The two numbers add to -20

⇒ x + y = -20

Rewrite x + y = -20 to make x the subject:

⇒ x = -20 - y

Substitute into xy = 64 and solve for y:

⇒ (-20 - y)y = 64

⇒ -20y - y² = 64

⇒ y² + 20y + 64 = 0

⇒ (y + 4)(y + 16) = 0

⇒ y = -4, y = -16

As x + y = -20

If y = -4 then x = -16

If y = -16 then x = -4

Therefore, the two numbers are -4 and -16