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Grade 8Magical Mathematics[Interesting Approach]

Respected Sir,
Please solve the attached question .

Question image for Respected Sir, Please solve the attached question

Siddhant

7 Years agoGrade 8

1 Answer

Dr Bhishma Hazarika

7 Years ago

Let n=2, so we will take only two number and their reciprocal

i.e b₁ , b₂and 1/b₁,1/b₂

We know AM>=GM for first two numbers

So b₁+b₂>=2(b₁b₂)^1/2.......................(1)

Now , For 1/b₁ and 1/b₂

(1/b₁+1/b₂)>=2(1/b₁b₂)^1/2.....................(2)

Now multiply Eq. (1) and Eq. (2)

(b₁+b₂)(1/b₁+1/b₂)>=4(b₁b₂)^1/2(1/b₁b₂)^1/2=4.1=4=2²

Now if n=3 then your answer will be 3²

Finally, AM and GM inequality is true for every natural value of n, i.e n=1,2,3,4,5,6.............

So your generalised answer is n²

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