Question

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

Answer 1

Answer: 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 = $\sqrt{24}$

    ⇒  (1/2)(x + y) = (1/2)($\sqrt{24}$)

    ⇒  [(1/2)x + (1/2)y]² = [(1/2)($\sqrt{24}$)]²

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

    ⇒  [(1/2)x + (1/2)y]² = 6

Answer 2

Answer:

Required value of ( 1/2x +1/2y)² is $\frac{6}{25}$

Step-by-step explanation:

Given,

${x}^{2} + {y}^{2} = 14$

and $xy = 5$

Now,

${( \frac{1}{2x} + \frac{1}{2y} ) }^{2} \\ = {( \frac{1}{2x}) }^{2} + 2 \times \frac{1}{2x} \times \frac{1}{2y} + {( \frac{1}{2y}) }^{2} \\ = \frac{1}{4 {x}^{2} } + \frac{1}{2xy} + \frac{1}{4 {y}^{2} } \\ = \frac{ {y}^{2} + {x}^{2} }{4 {x}^{2} {y}^{2} } + \frac{1}{2xy} \\ = \frac{14}{4 \times {5}^{2} } + \frac{1}{2 \times 5} \\ = \frac{7}{2 \times {5}^{2} } + \frac{1}{2 \times 5} \\ = \frac{7 + 5}{2 \times {5}^{2} } \\ = \frac{12}{2 \times {5}^{2} } \\ = \frac{6}{ {5}^{2} } \\ = \frac{6}{25}$

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549

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