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Answer 1

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

Answer 2

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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