Question

11．已知x+y=$\sqrt{3}+\sqrt{2}$，xy=$\sqrt{6}$，則x²+y²的值為（　�。�

• A． 5
• B． 3
• C． 2
• D． 1

Answer 1

分析 由（x+y）²=x²+y²+2xy，得出x²+y²=（x+y）²-2xy，再帶入已知數(shù)據(jù)求解即可．

解答 解：x²+y²=（x+y）²-2xy
=（$\sqrt{3}+\sqrt{2}$）²-2$\sqrt{6}$
=3+2+2$\sqrt{6}$-2$\sqrt{6}$
=5．
故選A．

點(diǎn)評(píng) 本題考查了二次根式的化簡求值，解答本題的關(guān)鍵在于先對(duì)原式進(jìn)行恰當(dāng)?shù)幕�簡然后代入求值�?/p>