Question

If x² + y² = 14 and xy = 5, find the value of (1/2x + 1/2y)

Answer 1

Answer:

answer is 6

Step-by-step explanation:

Using (x + y)² = x² + y² + 2xy, we have

    ⇒  (x + y)² = 14 + (2 x 5)

    ⇒  (x + y)² = 14 + (2 x 5)

    ⇒  (x + y)² = 24

    ⇒  x + y = root 24

    ⇒  (1/2)(x + y) = (1/2)(root24)

    ⇒  [(1/2)x + (1/2)y]² = [(1/2)(root 24)]^2

    ⇒  [(1/2)x + (1/2)y]² = (1/4) x 24

    ⇒  [(1/2)x + (1/2)y]² = 6

follow me ✌✌✌✌

Answer 2

Answer:

√6

Step-by-step explanation:

As we know,

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

(x + y)^2 = 14 + 2*5

(x + y)^2 = 14 + 10

(x + y)^2 = 24

x + y = √24 = 2√6

Now, Multiplying both sides by 1/2:-

1/2(x + y) = 1/2(2√6)

1/2x + 1/2y = √6

Hence,

1/2x + 1/2y = √6

Hope, it helps you.....