Question

si x-y=√3 xy=5 hallar x+y

Answer 1

Recuerda que:

${(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}$

${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

...

${(x - y)}^{2} = { \sqrt{3} }^{2} \\ {x}^{2} - 2xy + {y}^{2} = 3 \\ {x}^{2} + {y}^{2} = 3 + 2xy \\ {x}^{2} + {y}^{2} = 3 + 2(5) \\ {x}^{2} + {y}^{2} =13 \\ {x}^{2} +10 + {y}^{2} = 13 + 10 \\ {x}^{2} + 2xy + {y}^{2} = 23 \\ {(x + y)}^{2} = 23 \\ x + y = \sqrt{23}$