Question

If x = (7 – 4√3), find the value of √x + (1/√x)

Answer 1

Answer:

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Explanation:

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Answer 2

√x + 1/√x = 4

Explanation:

Given x = 7 + 4√3 -----(1)

Then 1/ x = 1 / (7 +4√3) -----(2)

Multiplying both numerator and denominator by (7 – 4√3),

we get:

1/ x = (7 – 4√3) / [(7 +4√3) 8 (7 – 4√3)]

1/ x = (7 – 4√3) / (49 – 48) = (7 – 4√3) / 1 = (7 – 4√3)

(√x + 1/√x )^2 = x + 1/x + 2

Substituting values from equation 1 & 2, we get:

(√x + 1/√x )^2  = (7 + 4√3) + (7 – 4√3) + 2 = 7 + 7 + 2 = 16

(√x + 1/√x)^2 = 16

Therefore √x + 1/√x = 4