Answer:
10
Step-by-step explanation:
[tex]2(x + y)^{2} = 116 \\ {(x + y)}^{2} = \frac{116}{2} \\ {(x + y)}^{2} = 58....(1) \\ xy = 24.....(2) \\ \because \: {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ \therefore \: 58 = {x}^{2} + {y}^{2} + 2 \times 24 \\ \therefore \: 58 = {x}^{2} + {y}^{2} + 48 \\ \therefore \: {x}^{2} + {y}^{2} = 58 - 48 \\ \huge \purple{ \boxed{\therefore \: {x}^{2} + {y}^{2} = 10}}[/tex]
