Math, asked by nithyanandham70, 1 year ago

If (1+√8)(1+√2)=a+b√2 then the value of a and b is

Answers

Answered by ali6503

Answer:

a+b=5 ———————(1)

Using (a+b)^2=a^2+b^2+2ab

=> 25=a^2+b^2+2×2

=> 25–4=a^2+b^2 = 21

Since (a-b)^2=a^2+b^2-2ab

Thus (a-b)^2=21–2×2=21–4=17

Thus a-b= (17)^1/2 —————(2)

Adding eqn (1) and (2),we get

2a=5+(17)^1/2

Thus a= [5+(17)^1/2]/2

And subtracting eqn (2) from (1) , we get

2b=5-(17)^1/2

Thus b=[5-(17)^1/2]/2

Hence a= [5+(17)^1/2]/2 and b=[5-(17)^1/2]/2

Step-by-step explanation:

Answered by Anonymous

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