Question

If x + y + z is equal to 9 and xy + y z + z x is equal to 40 find x square + y square + z square

Answer 1

Given,
x + y + z = 9 —-—-—-—1
xy + yz + zx = 40—-—-2

$\: \: \: \: \: \: {(x + y + z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2xy + 2yz + 2xz \\ = > {(x + y + z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2(xy + yz + xz) \\ From \: \: eq. 1 \: and \: 2, \\ = > {9}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2 \times 40 \\ = > {x}^{2} + {y}^{2} + {z}^{2} = 81 - 80 = 1.$





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