Question

Solve the following equation.

If: $(x^2 + y^2) = 14$, and $xy = 5$,

find the value of $\frac{1}{2}x + \frac{1}{2}y$

Answer 1

Answer:

√6

Step-by-step explanation:

ATQ, x²+y²=14

xy=5

Use the algebraic identity,

(x+y)square =x²+y²+2xy

Now, put the values,

(x+y)square=14+2x(5)

(x+y)square=24

x+y=√24

x+y=2√6

Now move to the question,

1/2x +1/2y=?

1/2(x+y)=? (take 1/2 common from both)

now put the value of x+y =2√6 from the above.

1/2×2√6= √6

Hence, Answer is √6.

Answer 2

answer is 6

Step-by-step explanation:

${( \frac{1}{2}x + \frac{1}{2} y)}^{2} \\ \frac{1}{4} {x}^{2} + \frac{1}{4} {y}^{2} + 2 \frac{1}{2} x \frac{1}{2} y \\ \frac{ {x}^{2} }{4} + \frac{ {y}^{2} }{4} + \frac{xy}{2} \: \: \: \: \: \: (xy = 5) \\ \frac{ {x}^{2} }{4} + \frac{ {y}^{2} }{4} + \frac{5}{2} \\ \frac{ {x}^{2} + {y}^{2} + 10 }{4} \: \: \: \: \: \: \: \: \: ( {x}^{2} + {y}^{2} = 14) \\ \frac{14 + 10}{4} \\ \frac{24}{4} \\ 6 \: answer$