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Question : If a = 7 - 4√3, find the value of √a + (1/√a).
Answer :
a = 7 - 4√3
1/a = 1/ (7 - 4√3)
Rationalising the denominator,
= 7 + 4√3 / (7 - 4√3) (7 + 4√3)
= 7 + 4√3 / 49 - 48
1/a = 7 + 4√3
a + 1/a = (7 - 4√3) + (7 + 4√3) = 14
We know that,
(√a + 1/√a)² = a + 1/a + 2
(√a + 1/√a)² = 14 + 2
(√a + 1/√a)² = 16
√a + 1/a = 4
Answer : 4
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Answer:
Question :
Question : If a = 7 - 4√3, find the value of √a + (1/√a).
Answer :
a = 7 - 4√3
1/a = 1/ (7 - 4√3)
Rationalising the denominator,
= 7 + 4√3 / (7 - 4√3) (7 + 4√3)
= 7 + 4√3 / 49 - 48
1/a = 7 + 4√3
a + 1/a = (7 - 4√3) + (7 + 4√3) = 14
We know that,
(√a + 1/√a)² = a + 1/a + 2
(√a + 1/√a)² = 14 + 2
(√a + 1/√a)² = 16
√a + 1/a = 4
Answer : 4
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