Phiếu bài tập Toán 9
Ví dụ 2. Tính:
a)
2√3-√30
√5-√2 16 1+√6
1
5
+
h)
Chương III: Căn thức
√15-√20 √21-√7
+
2-√√3
1-√3
b)
6+2√3 2
+
√√√3+1 √√√5-√3
√8-2√15

Question

help vs moi hoc lam chi tiet aj

Divinity · Answer

`a)`
`A = (2sqrt(3) - sqrt(30)) / (sqrt(5) - sqrt(2)) - sqrt(1/6) + 5 / (1 + sqrt(6))`
`A = (sqrt(6) * (sqrt(2) - sqrt(5))) / (sqrt(5) - sqrt(2)) - sqrt(6) / 6 + (5(sqrt(6) - 1)) / ((sqrt(6) + 1)(sqrt(6) - 1))`
`A = -sqrt(6) - sqrt(6) / 6 + (5(sqrt(6) - 1)) / (6 - 1)`
`A = -sqrt(6) - sqrt(6) / 6 + (5(sqrt(6) - 1)) / 5`
`A = -sqrt(6) - sqrt(6) / 6 + sqrt(6) - 1`
`A = -sqrt(6) / 6 - 1`
`b)`
`B = (6 + 2sqrt(3)) / (sqrt(3) + 1) - 2 / (sqrt(5) - sqrt(3)) + sqrt(8 - 2sqrt(15))`
`B = (2sqrt(3)(sqrt(3) + 1)) / (sqrt(3) + 1) - (2(sqrt(5) + sqrt(3))) / ((sqrt(5) - sqrt(3))(sqrt(5) + sqrt(3))) + sqrt((sqrt(5) - sqrt(3))^2)`
`B = 2sqrt(3) - (2(sqrt(5) + sqrt(3))) / (5 - 3) + |sqrt(5) - sqrt(3)|`
`B = 2sqrt(3) - (2(sqrt(5) + sqrt(3))) / 2 + sqrt(5) - sqrt(3)`
`B = 2sqrt(3) - (sqrt(5) + sqrt(3)) + sqrt(5) - sqrt(3)`
`B = 2sqrt(3) - sqrt(5) - sqrt(3) + sqrt(5) - sqrt(3)`
`B = 0`
`c)`
`C = sqrt(14) + 26 / (sqrt(14) - 1) - sqrt((5 - 3sqrt(14))^2)`
`C = sqrt(14) + (26(sqrt(14) + 1)) / ((sqrt(14) - 1)(sqrt(14) + 1)) - |5 - 3sqrt(14)|`
Do `5 = sqrt(25) 
`C = sqrt(14) + (26(sqrt(14) + 1)) / (14 - 1) - (3sqrt(14) - 5)`
`C = sqrt(14) + (26(sqrt(14) + 1)) / 13 - 3sqrt(14) + 5`
`C = sqrt(14) + 2(sqrt(14) + 1) - 3sqrt(14) + 5`
`C = sqrt(14) + 2sqrt(14) + 2 - 3sqrt(14) + 5`
`C = 7`
`h)`
`H = ((sqrt(15) - sqrt(20)) / (2 - sqrt(3)) + (sqrt(21) - sqrt(7)) / (1 - sqrt(3))) : 1 / (sqrt(7) - sqrt(5))`
`H = ((sqrt(5)(sqrt(3) - 2)) / (2 - sqrt(3)) + (sqrt(7)(sqrt(3) - 1)) / (1 - sqrt(3))) * (sqrt(7) - sqrt(5))`
`H = (-sqrt(5) - sqrt(7)) * (sqrt(7) - sqrt(5))`
`H = -(sqrt(7) + sqrt(5)) * (sqrt(7) - sqrt(5))`
`H = -((sqrt(7))^2 - (sqrt(5))^2)`
`H = -(7 - 5)`
`H = -2`
`i)`
`I = (4 / (sqrt(5) + 1) - 4 / (sqrt(5) - 1)) : sqrt(3 + 2sqrt(2))`
`I = ((4(sqrt(5) - 1) - 4(sqrt(5) + 1)) / ((sqrt(5) + 1)(sqrt(5) - 1))) : sqrt((sqrt(2) + 1)^2)`
`I = ((4sqrt(5) - 4 - 4sqrt(5) - 4) / (5 - 1)) : (sqrt(2) + 1)`
`I = (-8 / 4) : (sqrt(2) + 1)`
`I = -2 / (sqrt(2) + 1)`
`I = (-2(sqrt(2) - 1)) / ((sqrt(2) + 1)(sqrt(2) - 1))`
`I = (-2(sqrt(2) - 1)) / (2 - 1)`
`I = -2sqrt(2) + 2`
`j)`
`J = (1 / (sqrt(2) - 1) - 1 / (sqrt(2) + 1)) : sqrt(3 - 2sqrt(2))`
`J = (((sqrt(2) + 1) - (sqrt(2) - 1)) / ((sqrt(2) - 1)(sqrt(2) + 1))) : sqrt((sqrt(2) - 1)^2)`
`J = ((sqrt(2) + 1 - sqrt(2) + 1) / (2 - 1)) : (sqrt(2) - 1)`
`J = (2 / 1) : (sqrt(2) - 1)`
`J = 2 / (sqrt(2) - 1)`
`J = (2(sqrt(2) + 1)) / ((sqrt(2) - 1)(sqrt(2) + 1))`
`J = (2(sqrt(2) + 1)) / (2 - 1)`
`J = 2sqrt(2) + 2`

KhanhLinhw · Answer

`a)(2\sqrt{3} - \sqrt{30})/(\sqrt{5} - \sqrt{2}) - \sqrt{1/6} + 5/(1 + \sqrt{6})`
`= (-\sqrt{6}(\sqrt{5} - \sqrt{2}))/(\sqrt{5} - \sqrt{2}) - \sqrt{6}/6 + 5(\sqrt{6} - 1)/(6 - 1)`
`= -\sqrt{6} - \sqrt{6}/6 + \sqrt{6} - 1`
`= -1 - \sqrt{6}/6`
`b)(6 + 2\sqrt{3})/(\sqrt{3} + 1) - 2/(\sqrt{5} - \sqrt{3}) + \sqrt{8 - 2\sqrt{15}}`
`= (2\sqrt{3}(\sqrt{3} + 1))/(\sqrt{3} + 1) - (2(\sqrt{5} + \sqrt{3}))/(5 - 3) + \sqrt{(\sqrt{5} - \sqrt{3})^2}`
`= 2\sqrt{3} - (\sqrt{5} + \sqrt{3}) + (\sqrt{5} - \sqrt{3})`
`= 2\sqrt{3} - \sqrt{5} - \sqrt{3} + \sqrt{5} - \sqrt{3}`
`= 0`
`c)\sqrt{14} + 26/(\sqrt{14} - 1) - \sqrt{(5 - 3\sqrt{14})^2}`
`= \sqrt{14} + (26(\sqrt{14} + 1))/(14 - 1) - |5 - 3\sqrt{14}|`
`= \sqrt{14} + 2(\sqrt{14} + 1) - (3\sqrt{14} - 5)`
`= \sqrt{14} + 2\sqrt{14} + 2 - 3\sqrt{14} + 5`
`= 7`
`h)(( \sqrt{15} - \sqrt{20} )/(2 - \sqrt{3}) + ( \sqrt{21} - \sqrt{7} )/(1 - \sqrt{3})) : (1/(\sqrt{7} - \sqrt{5}))`
`= (( -\sqrt{5}(2 - \sqrt{3}) )/(2 - \sqrt{3}) + ( -\sqrt{7}(1 - \sqrt{3}) )/(1 - \sqrt{3})) . (\sqrt{7} - \sqrt{5})`
`= (-\sqrt{5} - \sqrt{7}) . (\sqrt{7} - \sqrt{5})`
`= -(\sqrt{7} + \sqrt{5})(\sqrt{7} - \sqrt{5})`
`= -(7 - 5)`
`= -2`
`i)(4/(\sqrt{5} + 1) - 4/(\sqrt{5} - 1)) : \sqrt{3 + 2\sqrt{2}}`
`= ((4\sqrt{5} - 4 - 4\sqrt{5} - 4)/4) : (\sqrt{2} + 1)`
`= (-8/4) : (\sqrt{2} + 1)`
`= -2/(\sqrt{2} + 1)`
`= -2(\sqrt{2} - 1)/(2 - 1)`
`= -2\sqrt{2} + 2`
`j)(1/(\sqrt{2} - 1) - 1/(\sqrt{2} + 1)) : \sqrt{3 - 2\sqrt{2}}`
`= (((\sqrt{2} + 1) - (\sqrt{2} - 1))/(2 - 1)) : \sqrt{(\sqrt{2} - 1)^2}`
`= ((\sqrt{2} + 1 - \sqrt{2} + 1)/1) : (\sqrt{2} - 1)`
`= 2/(\sqrt{2} - 1)`
`= 2(\sqrt{2} + 1)/(2 - 1)`
`= 2\sqrt{2} + 2`

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