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

If x + y = √3 and x - y = √2, then the value of 8xy(x2 + y2) is? Correct Answer 5

$$\eqalign{ & x + y = \sqrt 3 \,.......{\text{(i)}} \cr & x - y = \sqrt 2 \,.......(ii) \cr & {\text{From equation (i) and (ii)}} \cr & x = \frac{{\sqrt 3 + \sqrt 2 }}{2} \cr & y = \frac{{\sqrt 3 - \sqrt 2 }}{2} \cr & {\text{So, }}8xy\left( {{x^2} + {y^2}} \right) \cr & = 8 \times \frac{{\sqrt 3 + \sqrt 2 }}{2} \times \frac{{\sqrt 3 - \sqrt 2 }}{2}\left \cr & = 2\left( {3 - 2} \right)\left \cr & = 2 \times 1 \times \frac{{10}}{4} \cr & = 5 \cr} $$

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