Hướng dẫn trả lời:
Bài 1: Với x > y > 0:
1) `sqrt{xy} - x`
`= sqrt{x}cdot sqrt{y} - (sqrt{x})^2`
`= sqrt{x}cdot(sqrt{y} - sqrt{x})`
2) `x + y - 2sqrt{xy}`
`= x - 2sqrt{xy} + y`
`= (sqrt{x})^2 - 2cdot sqrt{x}cdot sqrt{y} + (sqrt{y})^2`
`= (sqrt{x} - sqrt{y})^2`
Giải thích:
Áp dụng HĐT `(A - B)^2 = A^2 - 2AB + B^2`
3) `xsqrt{y} - ysqrt{x}`
`= sqrt{x^2y} - sqrt{xy^2}`
`= sqrt{xycdotx} - sqrt{xycdoty}`
`= sqrt{xy}cdot(sqrt{x} - sqrt{y})`
4) `2sqrt{5} - 2sqrt{10} - sqrt{3} + sqrt{6}`
`= 2sqrt{5}cdot1 - 2sqrt{5}cdot sqrt{2} - sqrt{3}cdot1 + sqrt{3}cdot sqrt{2}`
`= 2sqrt{5}cdot(1 - sqrt{2}) - sqrt{3}cdot(1 + sqrt{2})`
`= (2sqrt{5} - sqrt{3})cdot(1 + sqrt{2})`
5) `sqrt{35} - sqrt{14}`
`= sqrt{7}cdot sqrt{5} - sqrt{7}cdot sqrt{2}`
`= sqrt{7}cdot(sqrt{5} - sqrt{2})`
6) `sqrt{xy} + 2sqrt{x} - 3sqrt{y} - 6`
`= (sqrt{xy} + 2sqrt{x}) - (3sqrt{y} + 6)`
`= sqrt{x}(sqrt{y} + 2) - 3cdot(sqrt{y} + 2)`
`= (sqrt{x} - 3)cdot(sqrt{y} + 2)`
7) `7 + 2sqrt{10}`
`= 5 + sqrt{10} + 2`
`= (sqrt{5})^2 + 2cdot sqrt{5}cdot sqrt{2} + (sqrt{2})^2`
`= (sqrt{5} + sqrt{2})^2`
Giải thích:
Áp dụng HĐT `(A + B)^2 = A^2 + 2AB + B^2`
8) `5 - 2sqrt{6}`
`= 3 - 2sqrt{6} + 2`
`= (sqrt{3})^2 - 2cdot sqrt{3}cdot sqrt{2} + (sqrt{2})^2`
`= (sqrt{3} - sqrt{2})^2`
Giải thích:
Áp dụng HĐT `(A - B)^2 = A^2 - 2AB + B^2`
9) `sqrt{x^2 - y^2} - x + y`
`= sqrt{(x + y)cdot(x - y)} - (x - y)`
`= sqrt{(x + y)cdot(x - y)} - (sqrt{x - y})^2`
`= sqrt{x - y}cdot(sqrt{x + y} - sqrt{x - y})`
Giải thích:
Áp dụng HĐT `A^2 - B^2 = (A + B)cdot(A - B)`
10) `3x - 2sqrt{x}`
`= 3(sqrt{x})^2 - 2sqrt{x}`
`= sqrt{x}cdot(3sqrt{x} - 2)`
