Verified answer

Step-by-step explanation:

Solution (a) :-

x + y = 9 ----------(1)

xy = 5

Squaring on both sides of eq (1), we get

[tex]\sf \: (x + y) {}^{2} = (9) {}^{2} \\ \\ \sf \: {x}^{2} + {y}^{2} + 2xy = 81 \\ \\ \sf \: {x}^{2} + {y}^{2} + 2(5) = 81 \\ \\ \sf \: {x}^{2} + {y}^{2} = 81 - 10 \\ \\ \implies \: \bf \: {x}^{2} + {y}^{2} = 71[/tex]

Solution (b) :-

x - y = 14 -----------(1)

xy = 48

Squaring on both sides of eq (1),

[tex]\sf \: (x - y) {}^{2} = {14}^{2} \\ \\ \sf \: {x}^{2} + {y}^{2} - 2xy = 196 \\ \\ \sf \: {x}^{2} + {y}^{2} - 2(48) = 196 \\ \\ \sf \: {x}^{2} + {y}^{2} = 196 + 96 \\ \\ \implies \: \bf \: {x}^{2} + {y}^{2} = 292[/tex]

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