Question

If x +y = √3 and x - y = √2, then the value of 8xy (x2 + y2) is

A) 6 B) √6 C) 5 D) √5

Answer 1

Answer:

option C is the answer for the given problem

Answer 2

$x + y = \sqrt{3} \\ ( {x + y})^{2} = 3 \\ {x}^{2} + {y}^{2} + 2xy = 3...(1) \\ \\ x - y = \sqrt{2} \\ ( {x - y})^{2} = 2 \\ {x}^{2} + {y}^{2} - 2xy = 2...(2) \\ \\ (1) + (2) \\ 2( {x}^{2} + {y}^{2} ) = 5 \\ {x}^{2} + {y}^{2} = \frac{5}{2} \\ \\ from \: \: (1) \\ {x}^{2} + {y}^{2} + 2xy = 3 \\ \frac{5}{2} + 2xy = 3 \\ 2xy = 3 - \frac{5}{2} \\ xy = \frac{1}{4} \\ \\ \\ 8xy( {x}^{2} + {y}^{2} ) = 8 \times \frac{1}{4} ( \frac{5}{2} ) \\ = 5$