Question

if x=11-2√30 then find (a)√x+1/√x (b) √x-1/√x​

Answer 1

Answer:

a) √x + 1/ √x =2 √6

b) √x - 1/ √x = -2√5

Step-by-step explanation:

Given---> x=11 - 2√30

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To find--->

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a) √x + 1/√x

b) √x - 1/√x

Solution--->

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We have

x = 11 -2√30

=6 + 5 - 2√(6 × 5)

=(√6)² + ( √5)² - 2 √6 √5

=> x =( √6 - √5 )²

Now

√x = √(√6 - √5)²

= √6 - √5

1/√x = 1/(√6 - √5)

Multiplying by (√6 +√ 5) in numreator and denominator

1/√x = (√6+√5) / (√6 - √5) (√ 6 + √5 )

=(√6 + √5 ) / ( √6)² - ( √5)²

=(√6 + √ 5 ) /( 6 - 5)

= (√6 + √5) /1

= √6 + √ 5

Now

a) √x + 1/√x = (√6 - √ 5) + (√6 + √5)

+√ 5 and - √5 cancel out each other

√x + 1/√x = 2√6

b) √x - 1/ √x =(√6 - √ 5) - (√ 6 + √5)

= √6 - √5 - √6 - √5

+√6 and -√6 cancel out each other

√x - 1/√x =-2 √5

Answer 2

Answer:

X2=11+2√ 30

X=√ (11+√ 30)

X=√ ((√ 6)2+ (√ 5)2+ (2×√ 6×√ 5))

X=√6+√5