Question

if x2 + y2 = 51 and x -y =7, evaluate xy

Answer 1

Answer:

xy=1

Step-by-step explanation:

x-y=7

squaring on both sides

(x-y) 2=49

x2+y2-2xy=49

51-2xy=49

2xy=2

xy=1

Answer 2

x - y = 7

Now we know that when we subtract 'x' and 'y' we get 7 so now we will square the LHS and RHS

⇒ (x - y)² = 7²

According to the algebraic indentity we have to use this ⇒ (a - b)² = a²-2ab-b²

Now how is this identity derived is the question. Let's see how we got his identity.

⇒ (a - b)²

⇒ (a - b) (a - b)

⇒ a (a - b) - b (a - b)

⇒ a(a) - a(b) - b(a) - b(b)

⇒ a² - ab - ba + b²

⇒ a² - ab - ab + b²

⇒ a² - 2ab + b²

So now our equation will become as follows.

x² - 2xy + y² = 49

x² + y² - 2xy = 49

Now according to the question, x² + y² = 51 so we must substitute the value.

⇒ 51 - 2xy = 49

⇒ 51 - 2xy - 51 = 49 - 51

⇒ -2xy = -2

⇒ -2xy ÷ -2 = -2 ÷ -2

⇒ xy = 1

∴ The value for xy in the following question would be 1.