Question

Class 9 Mathematics Number System
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Answer 1

Given :-

x = 1/(3 - √5)

So , 1/x = 1/(1/(3-√5))

=> 3 - √5

Since in the denominator of the value of x is a root , We have to rationalize it

So,

x = 1/(3 - √5)

=> 1 x (3 + √5)/(3 - √5)(3 + √5)

=> (3 + √5)/(3)² - (√5)²

[ By identity :- (a +b)(a - b) = a² - b² ]

=> (3 + √5)/(9 - 5)

=> (3 + √5)/4

Now ,

x + 1/x = (√x)² + (1/√x)² + (2 )x (√x) x (1/x) - (2) x (√x) x (1/√x)

By solving the both sides will be equal to each other

Now ,

We have the values of x and 1/x , so we can put it in the above equation

(3 + √5)/4 + (3 - √5) = (√x + 1/√x) - (2) x (√x) x (1/√x)

=>(3 + √5 + 12 - 4√5)/4 = (√x + 1/√x) - 1

=> (15 - 3√5 )/4 = (√x + 1/√x)

=> (15 - 3√5)/4 + 1 = (√x + 1/√x)

=> (15 - 3√5 + 4)/4 = (√x + 1/√x)

=> (19 - 3√5)/4 = (√x + 1/√x)

This is the final answer

Hence , solved .

Hope it helped you