If x = 3+√8 find the value of √x+1/√x
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Answered by
3
(√x+1/√x)^2=x+1/x+2
=3+√8+(1/(3+√8))+2
(a+b)(a-b) =a^2-b^2
(3+√8)(3-√8)=9-8
=3+√8+3-√8+2
=8
√x+1/√x=√8=2√2
=3+√8+(1/(3+√8))+2
(a+b)(a-b) =a^2-b^2
(3+√8)(3-√8)=9-8
=3+√8+3-√8+2
=8
√x+1/√x=√8=2√2
Answered by
2
x = 3 + sqrt 8 = 3 + 2 sqrt 2
sqrt x = sqrt a + sqrt b
x = a + b + 2 sqrt (a b)
So. a+b = 3. ab = 2
(a-b)^2 = 3^2 - 4 * 2 = 1
a-b = 1 or -1
a = 2, b= 1
Sqrt x = 1 + sqrt 2
1/sqrt(x) = sqrt(2) - 1. By rationalizing denominator.
ANSWER = 2 sqrt2
sqrt x = sqrt a + sqrt b
x = a + b + 2 sqrt (a b)
So. a+b = 3. ab = 2
(a-b)^2 = 3^2 - 4 * 2 = 1
a-b = 1 or -1
a = 2, b= 1
Sqrt x = 1 + sqrt 2
1/sqrt(x) = sqrt(2) - 1. By rationalizing denominator.
ANSWER = 2 sqrt2
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