Question

a)A=\(\sqrt{12-6\sqrt{3}}+\sqrt{21-12\sqrt{3}}\)
b)B=\(\sqrt{19+4\sqrt{15}}+\sqrt{19-4\sqrt{15}}\)
c)C=\(\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}\)
d)chứng minh rằng:\(\sqrt{7+4\sqrt{3}}+\sqrt{7-4\sqrt{3}}\) là số nguyên

Answer 1

`a)A=\sqrt{12-6\sqrt{3}}+\sqrt{21-12\sqrt{3}}`

`A=\sqrt{(3-\sqrt{3})^2}+\sqrt{(2\sqrt{3}-3)^2}`

`A=|3-\sqrt{3}|+|2\sqrt{3}-3|`

`A=3-\sqrt{3}+2\sqrt{3}-3=\sqrt{3}`

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`b)B=\sqrt{19+4\sqrt{15}}+\sqrt{19-4\sqrt{15}}`

`B=\sqrt{(\sqrt{15}+2)^2}+\sqrt{(\sqrt{15}-2)^2}`

`B=|\sqrt{15}+2|+|\sqrt{15}-2|`

`B=\sqrt{15}+2+\sqrt{15}-2=2\sqrt{15}`

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`c)C=\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}`

`C=\sqrt{(\sqrt{5}-\sqrt{3})^2}-\sqrt{(\sqrt{5}+\sqrt{3})^2}`

`C=|\sqrt{5}-\sqrt{3}|-|\sqrt{5}+\sqrt{3}|`

`C=\sqrt{5}-\sqrt{3}+\sqrt{5}+\sqrt{3}=2\sqrt{5}`

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`d)\sqrt{7+4\sqrt{3}}+\sqrt{7-4\sqrt{3}}`

`=\sqrt{(2+\sqrt{3})^2}+\sqrt{(2-\sqrt{3})^2}`

`=|2+\sqrt{3}|+|2-\sqrt{3}|`

`=2+\sqrt{3}+2-\sqrt{3}=4`

    `=>Đpcm`

`

Answer 2

Cho tam giác ABC vuông tại B đường cao BK vẽ hình và ghi giải thích kết luận theo nội dung định lý 1