Toán Lớp 9: Chứng minh √(7 – 2√10) – √(8 – 2√15) + √2 = √3
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Toán Lớp 9: Chứng minh √(7 – 2√10) – √(8 – 2√15) + √2 = √3
Comments ( 1 )
=\sqrt{5-2\sqrt{5}*\sqrt{2}+2}-\sqrt{5-2\sqrt{5}*\sqrt{3}+3}+\sqrt{2}
=\sqrt{(\sqrt{5}-\sqrt{2})^2}-\sqrt{(\sqrt{5}-\sqrt{3})^2}+\sqrt{2}
=|\sqrt{5}-\sqrt{2}|-|\sqrt{5}-\sqrt{3}|+\sqrt{2}
=\sqrt{5}-\sqrt{2}-\sqrt{5}+\sqrt{3}+\sqrt{2}
=\sqrt{3}=VP (đpcm)