if x(5+√7) is a rational number then x must be equal to
4 options
(1) 5+√7
(2)√7-5
(3) √7-√5
(4) 7+√5
Answers
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Given : x(5+√7) is a rational number
To Find : Value of x
(1) 5+√7
(2)√7-5
(3) √7-√5
(4) 7+√5
Solution:
x(5+√7) is a rational number
Check each options
(1) x = 5+√7
(5+√7)(5+√7) = 25 + 7 + 10√7 = 32 + 10√7 Irrational
(1) x = 5+√7
(5+√7)(5+√7) = 25 + 7 + 10√7 = 32 + 10√7 Irrational
(2) x = √7-5
(√7 -5)(5+√7) = 7-25 = -18 Rational
(3) x = √7-√5
(√7-√5)(5+√7) = 7 +5√7 - 5√5 -√35 Irrational
4) 7+√5
(7+√5)(5+√7) =35 + 7√7 + 5√5 + √35 Irrational
Hence x = √7-5 is correct option
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