If x= root 5+ root 3 divided by root 5 - root 3 then find the value of x+1/x
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8
Step-by-step explanation:
x = (root 5+ root 3) / (root 5 - root 3)
Therefore, x + 1/x = (root 5+ root 3) / (root 5 - root 3) + (root 5 - root 3) / (root 5+ root 3)
⇒ x + 1/x = [ (root 5+ root 3)² + (root 5 - root 3)² ] / [ (root 5)² - (root 3)² ]
= [ (root 5+ root 3)² + (root 5 - root 3)² ] / [ 2 ]
= 2(root 5)² + 2(root 3)² / [ 2 ]
= (root 5)² + (root 3)²
= 5 + 3
= 8
Hope it helps!!
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