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Diano4ka-milaya [45]
3 years ago
11

Show by substitution that(5-i√5)/5 is a solution to 5x²-10x+6=0.

Mathematics
1 answer:
svetoff [14.1K]3 years ago
8 0

Answer:

Putting the value of x = (5-i√5)÷5 in 5x²-10x+6=0.

We get,

5(\dfrac{(5-i\sqrt{5})}{5} )^2-10(\dfrac{(5-i\sqrt{5})}{5} ) +6=0\\\\\dfrac{(5-i\sqrt{5})}{5} ^2-2(5-i\sqrt{5} ) +6=0\\\\(5-i\sqrt{5}) ^2-10(5-i\sqrt{5} ) +30=0

⇒ 25 + (i√5)² - 10i√5 - 50 + 10i√5 + 30 = 0

⇒ (i√5)² + 5 = 0       {∵ i² = -1}

⇒ - 5 + 5 = 0

⇒ 0 = 0

Thus, (5-i√5) ÷ 5 is the solution of 5x²-10x+6=0.

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Construct the cumulative frequency distribution for the given data.
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Answer:

       Age                               Frequency                   Cumulative Frequency

 Less than 30                             27                                       27

 Less than 40                             37                                27 + 37  =  64

 Less than 50                              1 1                                 64 + 11   =  75

 Less than 60                               3                                  75 + 2   =  77

 Less than 70                               5                                   77 + 5   =  82

 Less than 80                               1                                     82 + 1  =  83

 Less than 90                              2                                    83 +2  =  85

Step-by-step explanation:

Given:

The Frequency Distribution table of ages of best actresses when award was won

To find:

Construct the cumulative frequency distribution

Solution:

In order to construct cumulative frequency distribution for the given data, each frequency from above table is added to the sum of the previous frequencies. For example, frequency for Less than 40  is 37 and the previous frequency (less than 30) is 27 so in order to calculate cumulative frequency 27 i.e. previous frequency is added to 37 (frequency of less than 30). The complete table is given above.

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