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Find `a` and `b` such that `a,b` are real numbers and
`(6sqrt3-sqrt5)/(2sqrt5)= a + b sqrt15`. (2 marks)
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`a= -1/2, \ b=3/5`
| `(6sqrt3-sqrt5)/(2sqrt5)` | `=(6sqrt3-sqrt5)/(2sqrt5) xx (2sqrt5)/(2sqrt5)` | |
| `=(2sqrt5(6sqrt3 – sqrt5))/(4 xx5)` | ||
| `=(12sqrt15-10)/20` | ||
| `=- 1/2 + 3/5 sqrt15` |
`:. a= -1/2, \ b=3/5`
Find `a` and `b` such that `a,b` are real numbers and
`(sqrt3-2)/(2sqrt3)= a + b sqrt3`. (2 marks)
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`a = 1/2, \ b = – 1/3`
| `(sqrt3-2)/(2sqrt3)` | `= (sqrt3-2)/(2sqrt3) xx (2sqrt3)/(2sqrt3)` |
| `= (2sqrt3(sqrt3-2))/(4 xx 3)` | |
| `= (6-4sqrt3)/12` | |
| `=1/2 – 1/3 sqrt3` |
`:.\ a = 1/2, \ b = – 1/3`
Find `a` and `b` such that `a, b` are real numbers and
`(8-sqrt27)/(2sqrt3) = a + bsqrt3`. (2 marks)
`:. a =-3/2, \ b = 4/3`
| `(8-sqrt27)/(2sqrt3) xx (2sqrt3)/(2sqrt3)` | `=(2sqrt3(8-3sqrt3))/(2sqrt3)^2` |
| `= (16sqrt3-18)/12` | |
| `= -3/2 + 4/3sqrt3` |
`:. a = -3/2, \ b = 4/3`