Question

2．已知x=$\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$，y=$\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$，求代數(shù)式2x²-4xy+2y²的值．

Answer 1

分析 先化簡(jiǎn)x，y的值，再把x，y的值代入代數(shù)式2x²-4xy+2y²即可．

解答 解：∵x=$\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$=5+2$\sqrt{6}$，
y=$\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$=5-2$\sqrt{6}$，
∴原式=2（x²-2xy+y²） 
=2（x-y）²
=2（5+2$\sqrt{6}$-5+2$\sqrt{6}$）²
=2（4$\sqrt{6}$）²
=2×96
=192．

點(diǎn)評(píng) 本題考查了二次根式的化簡(jiǎn)求值，先化簡(jiǎn)x，y的值是解題的關(guān)鍵．