Question

if p = √2-√5 / √2+√5 and q=√2+√5 / √2-√5 , find the value of (i) p-q and (ii) p²-q²​

Answer 1

Heythere ‼

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pp = ( 2 – √5 ) / ( 2 + √5 )

= ( 2 – √5 ) / ( 2 + √5 ) × ( 2 – √5 ) / ( 2 – √5 )

= ( 2 – √5 )² / ( 2² – √5² )

= ( 4 – 4√5 + 5 ) / ( 4 – 5 )

= 9 – 4√5

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qq = ( 2 + √5 ) / ( 2 – √5 )

= ( 2 + √5 ) / ( 2 – √5 ) × ( 2 + √5 ) / ( 2 + √5 )

= ( 2 + √5 )² / ( 2² – √5² )

= ( 4 + 4√5 + 5 ) / ( 2 – 5 )

= 9 + 4√5

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Now, putting the values of p and q in the given equation :-

pp + qq = ( 9 – 4√5 ) + ( 9 + 4√5 )

= 9 – 4√5 + 9 + 4√5

= 18

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Answer 2

Answer:

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