Question

If 3+√8 by 3-√8 plus 3-√8by 3+ √8=a+b√2

Answer 1

Solution:

Given

LHS =

[(3+√8)/(3-√8)]+[(3-√8)/(3+√8)]

= [(3+√8)²+(3-√8)²]/[(3-√8)(3+√8)]

= {2[3²+(√8)²]}/[3²-(√8)²]

/* we know the algebraic identity:

i) (a+b)²+(a-b)² = 2(a²+b²)

ii)(a+b)(a-b) = a²-b² */

= [2(9+8)]/(9-8)

= (2×17)/1

= 34

Now ,

LHS = RHS

=> 34 = a+b√2 [given ]

=> 34 + 0×√2 = a+b√2

Compare both sides , we get

=> a = 34 , b = 0

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