Question

find the value x to the power of 2+ y to the power of 2,if x+y=6,xy=8​

Answer 1

Required Answer:-

Given:

• x + y = 6
• xy = 8

To find:

• The value of x² + y²

Solution:

Given that,

➡ x + y = 6 .....(i)

➡ xy = 8

Squaring both sides of equation (i), we get,

➡ (x + y)² = 36

➡ x² + y² + 2xy = 36

Substituting the value of xy, we get,

➡ x² + y² + 2 × 8 = 36

➡ x² + y² + 16 = 36

➡ x² + y² = 36 - 16

➡ x² + y² = 20

Hence, the value of x² + y² is 20.

Answer:

• x² + y² = 20

Identity Used:

➡ (x + y)² = x² + 2xy + y²

Other Identities:

➡ (x - y)² = x² - 2xy + y²

➡ x² - y² = (x + y)(x - y)

➡ (x + y)² = (x - y)² + 4xy

➡ (x - y)² = (x + y)² - 4xy

➡ (x + y)² + (x - y)² = 2(x² + y²)

➡ (x + y)² - (x - y)² = 4xy

Answer 2

Question : Find the value of x² + y², if x + y = 6 and xy = 8

Given : x + y = 6 and xy = 8

To Find : Value of x² + y²

Answer : x² + y² = 20

____________________________________________________

• We need to use an algebraic identify to solve this question and that identify will (a + b)² = a² + b² + 2ab

Process to Solve :

First We Take x and y in place of a and b in the algebraic identify used , Then we expand it and substitute the values which are given. Transposing the constants leave us with x² + y², and Finally we can find the value !!!

____________________________________________________

• Take x and y in place of a and b in (a + b)² = a² + b² + 2ab

⇒ (x + y)² = x² + y² + 2xy

• Substitute the value of x + y

⇒ (6)² = x² + y² + 2xy

⇒ 36 = x² + y² + 2xy

• Substitute the Value of xy

⇒ 36 = x² + y² + 2(8)

⇒ 36 = x² + y² + 16

⇒ 36 - 16 = x² + y²

⇒ 20 = x² + y²

• Switch Sides

⇒ x² + y² = 20