Question

IF X square + Y square is equal to 14 and X Y is equal to 5 find the value of 1 by 2 X + 1 by 2 y whole square ​

Answer 1

Answer:

$\frac{ \sqrt{6} }{5}$

Step-by-step explanation:

${x}^{2} + {y}^{2} = 14 \\ xy = 5 \\ {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ {(x + y)}^{2} = 14 + 2 \times 5\\ {(x + y)}^{2} = 14 + 10 \\ x + y = \sqrt{24} = \sqrt{2 \times 2 \times 2 \times 3} \\ = 2\sqrt{6} \\ \frac{1}{2x} + \frac{1}{2y} = \frac{2y + 2x}{2x \times 2y} \\ = \frac{2(x + y)}{4xy} \\ = \frac{x + y}{2xy} \\ = \frac{2 \sqrt{6} }{2 \times 5} = \frac{ \sqrt{6} }{5}$