KetZoomer KetZoomer
  • 11-12-2021
  • Mathematics
contestada

If [tex]x^{2} + y^{2} = 6[/tex] and [tex]x + y = \sqrt{7}[/tex], then what is [tex]x-y[/tex]?

Respuesta :

LammettHash
LammettHash LammettHash
  • 11-12-2021

Recall that

(x + y)² = x² + 2xy + y²

Then if x + y = √7 and x² + y² = 6, we have

(√7)² = 6 + 2xy   ⇒   2xy = 1

We also have

(x - y)² = x² - 2xy + y²

so that

(x - y)² = 6 - 1   ⇒   (x - y)² = 5

which means x - y has two possible values, √5 or -√5.

Answer Link

Otras preguntas

Diatomic molecules of gases are due to ___ bonds.
Samantha had 500 jars of slime 30% green 25% clear and 15% purple the rest of the jars of slime were blue how many jars were blue
asia's primary export to europe consisted of ___. A.gunpowder B.spices C. ceramics D. dried foods
What did many women do in mining towns? A) look for gold B) open boarding houses C) start churches D) work on railroads
Which equation represents a proportional relationship? y=13x+1 y = 3x + 7 14x+y=10 y=14x
what number has the same value as [5]
Can a human being be devoid (empty) of a human emotion ? Explain.
What type of anxiety might be alleviated by starting a 30 minute per day aerobic exercise program ? emotional physical behavioral mental
Which graph represents the same relation as the rule y = 2x, for all real numbers x?
The points ( - 6,4) and ( - 5,u) fall on a line with a slope of - 7. What is the value of u?