Question

if (x + y) = 9 and xy = 6, find the value of x² + y².​

Answer 1

Answer:

76.65

Step-by-step explanation:

$x + y = 9 \\ x = y - 9 \: \: \: \: \: \: \: \: (1)\\ xy = 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: (2) \\ substituting \: (1) \: in \: (2) \\ (y - 9) \times y = 6 \\ {y}^{2 } - 9y = 6 \\ solving \: the \: above \: equation \\ y = 8.275 \: and \: 0.725 \\ therefore \: x = \frac{6}{8.275 \:} \: and \frac{6}{0.725} \\ i.e. \: x \: can \: be \: 0.725 \: when \: y = 8.25 \\ x \: can \: be \: 8.725 \: when \: y = 0.725 \\ so \: {x}^{2} + {y}^{2} = {8.725}^{2} + {0.725}^{2} = 76.65$