Question

if x+y =12 and xy=32 then find the value of xpower2 + ypower2

Answer 1

Answer:

given, x+y = 12 and xy = 32

(6 this is power)

Step-by-step explanation:

(x+y)^2 = x^2 + y^2 + 2xy

(12)^2 = x^2 + y^2 + 2 X 32

(144) = x^2 + y^2 + 64

144-64 = x^2 + y^2

80 = x^2 + y^2

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Answer 2

Answer:

80

Step-by-step explanation:

Given -

• x + y = 12
• xy = 32-------1

To find -

• Value of x² + y²

Solution -

→ x + y = 12

→ x = 12 - y (putting in 1)

→(12 - y)y = 32

→ 12y - y² = 32

→ y² - 12y + 32 = 0

→ y² - 8y - 4y + 32 = 0

→ y(y - 8) - 4(y - 8) = 0

→ (y - 4)(y - 8) = 0

→ y = 4 , y = 8

Case A

y = 4 (putting in 1)

→ x(4) = 32

→ x = 32/4

→ x = 8

Now, x² + y² = (8)² + (4)²

= 64 + 16

= 80

Case B

y = 8 (putting in 1)

→ x(8) = 32

→ x = 32/8

→ x = 4

Now, x² + y² = (4)² + (8)²

= 16 + 64

= 80

Therefore, the value of x² + y² is 80.