Question

1) If x+y =2 and xy=1 then find x^4+y^4
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Answer 1

x^4+y^4 = 2

Step-by-step explanation:

$given \: that \\ x + y = 2 \\ squaring \: on \: both \: sides \\ {(x + y)}^{2} = {2}^{2} \\ {x}^{2} + {y}^{2} + 2xy = 4 \\ substitute \: x = 1 \\ {x}^{2} + {y}^{2} + 2(1) = 4 \\ {x}^{2} + {y}^{2} = 4 - 2 \\ {x}^{2} + {y}^{2} = 2 \\ again \: squaring \: on \: both \: sides \\ {( {x}^{2} + {y}^{2} ) }^{2} = {2}^{2} \\ {x}^{4} + {y}^{4} + 2 {x}^{2} {y}^{2} = 4 \\ {x}^{4} + {y}^{4} = 4 - 2 {(xy)}^{2} \\ {x}^{4} + {y}^{4} = 4 - 2(1) \\ {x}^{4} + {y}^{4} = 2$

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