১৮। $m+n = \sqrt{3}$ এবং $m-n = \sqrt{2}$ হলে— i. $mn = \frac{1}{4}$ ii. $m^{2} - n^{2} = \sqrt{6}$

Question

১৮। $m+n = \sqrt{3}$ এবং $m-n = \sqrt{2}$ হলে— i. $mn = \frac{1}{4}$ ii. $m^{2} - n^{2} = \sqrt{6}$ iii. $2(m^{2}+n^{2}) = 5$ নিচের কোনটি সঠিক?

Accepted Answer

i, ii ও iii

Explanation: $mn = \frac{(m+n)^{2} - (m-n)^{2}}{4} = \frac{1}{4}$, $m^{2} - n^{2} = (m+n)(m-n) = \sqrt{6}$, এবং $2(m^{2}+n^{2}) = (m+n)^{2} + (m-n)^{2} = 5$।

১৮। $m+n = \sqrt{3}$ এবং $m-n = \sqrt{2}$ হলে— i. $mn = \frac{1}{4}$ ii. $m^{2} - n^{2} = \sqrt{6}$ iii. $2(m^{2}+n^{2}) = 5$ নিচের কোনটি সঠিক?

ব্যাখ্যা (Explanation):

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১৮। m+n=3m+n = \sqrt{3}m+n=3​ এবং m−n=2m-n = \sqrt{2}m−n=2​ হলে— i. mn=14mn = \frac{1}{4}mn=41​ ii. m2−n2=6m^{2} - n^{2} = \sqrt{6}m2−n2=6​ iii. 2(m2+n2)=52(m^{2}+n^{2}) = 52(m2+n2)=5 নিচের কোনটি সঠিক?

ব্যাখ্যা (Explanation):

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১৮। $m+n = \sqrt{3}$ এবং $m-n = \sqrt{2}$ হলে— i. $mn = \frac{1}{4}$ ii. $m^{2} - n^{2} = \sqrt{6}$ iii. $2(m^{2}+n^{2}) = 5$ নিচের কোনটি সঠিক?