Question

If x+y = 20, xy = 34, then find the value of x + y?. Solution:

Answer 1

x-y = √(x+y)²-4xy = √(400 - 4 x 34) = √(400 - 136) = √264 = 2√66

Answer 2

$x + y = 20 \\ = > x = 20 - y \\ again \\ xy = 34 \\ = > (20 - y)y = 34 \: (substituting \: the \: value \: of \: x) \\ = > 20y - {y}^{2} - 34 = 0 \\ = > - {y}^{2} + 20y - 34 = 0 \\ = > {y}^{2} - 20y +34 = 0 \\ \\ by \:using \: quadratic \: formula - \\ x = \frac{ - b \binom{ + }{ - } \sqrt{ {b}^{2} - 4ac} }{2a} \\ \: \: \: \: = \frac{ - ( - 20) \binom{ + }{ - } \sqrt{ {( - 20)}^{2} - 4 \times 1 \times 34 } }{2 \times 1} \\ \: \: \: \: = \frac{20 \binom{ + }{ - } \sqrt{400 - 136} }{2} \\ \: \: \: \: = \frac{20 \binom{ + }{ - } \sqrt{264} }{2} \\ \\ so \: required \: roots \: are - \\ \\ \frac{20 - \sqrt{264} }{2} \: \: \: \: \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: \: \frac{20 + \sqrt{264} }{2}$

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