Question

x+y =2 x×y=1 find x4+y4​

Answer 1

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Answer 2

$\sf x + y = 2$

squaring on both sides

$\sf{ {(x + y)}^{2} = {2}^{2} }$

$\sf{ {x}^{2} + {y}^{2} + 2xy= 4 }$

$\sf{ {x}^{2} + {y}^{2} + 2(1)= 4 }$

$\sf{ {x}^{2} + {y}^{2} = 4 - 2}$

$\sf{ {x}^{2} + {y}^{2} = 2}$

Now again, squaring on both sides

$\sf{{( {x}^{2} + {y}^{2} )}^{2} = {2}^{2} }$

$\sf{ {x}^{4} + {y}^{4} + 2(1)= 4}$

$\sf{ {x}^{4} + {y}^{4} = 4 - 2}$

$\fbox{\sf{ {x}^{4} + {y}^{4} = 2}}$