how do you solve if x(5+root7) is a rational number then x must be equal to?
回答 (3)
2020-07-23 7:39 pm
Let x = a + b√7, where a and b are real numbers.
(a + b√7)(5 + √7)
= 5a + a√7 + 5b√7 + 7b
= (5a + 7b) + (a + 5b)√7
When (a + b√7)(5 + √7) is real, a + 5b = 0
Then, a = -5b
When b = -n: a = 5n, where n is any real number
x = 5n - n√7
where n is any real number
(a + b√7)(5 + √7)
= 5a + a√7 + 5b√7 + 7b
= (5a + 7b) + (a + 5b)√7
When (a + b√7)(5 + √7) is real, a + 5b = 0
Then, a = -5b
When b = -n: a = 5n, where n is any real number
x = 5n - n√7
where n is any real number
2020-07-23 7:52 pm
x(5 + √7) = a/b . . . . . . where a and b are integers
x = a/b(5 + √7)
ie x is any rational number dived by (5 + √7)
x = a/b(5 + √7)
ie x is any rational number dived by (5 + √7)
2020-07-23 7:24 pm
the rational number divided with 5 + root7.
I don't get the purpose of the question.
I don't get the purpose of the question.
收錄日期: 2021-04-18 18:34:17
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