Answered

IDNLearn.com provides a user-friendly platform for finding and sharing knowledge. Ask anything and receive comprehensive, well-informed responses from our dedicated team of experts.

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

Sagot :

Semsee45idn

Answer:

-4 and -16

Step-by-step 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

Let they be a and b

  • a+b=-20--(1)
  • ab=64

So

[tex]\\ \rm\rightarrowtail (a-b)^2=(a+b)^2-4ab[/tex]

[tex]\\ \rm\rightarrowtail (a-b)^2=(-20)^2-4(64)=400-256=144[/tex]

[tex]\\ \rm\rightarrowtail a-b=12\dots(2)[/tex]

From both equations

  • 2a=-8=>a=-4
  • -4+b=-20
  • b=-16
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.