Question

If x=√7+√3, show that x-4/x=2√3

Answer 1

Answer:

9.67840488150122

Step-by-step explanation:

Given :

x=7–√+43–√

⟹1x=17–√+43–√

⟹1x=1(7–√+43–√)(7–√−43–√)(7–√−43–√)

(a+b)(a−b)=a2−b2

Therefore,

⟹1x=7–√−43–√(7–√)2−(43–√)2

⟹1x=7–√−43–√−41

⟹x+1x=7–√+43–√−7–√−43–√41

⟹x+1x=417–√+1643–√−7–√+43–√41

⟹x+1x=857–√+213–√41

Exact answer :

x+1x=857–√+213–√41

Decimal Approximation :

x+1x=9.67840488150122...

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