5. a" + bn If -n-1 . an-t is the G....
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5. a" + bn If -n-1 . an-t is the G.M.'s between a and b, then 6. find the value of n. [NCERT)

JEE/Engineering Exams
Maths
Solution
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( frac{a^{m}+b^{4}}{a^{n-1}+b^{n+}}=sqrt{a b} ) ( a^{n}+b^{4}=(a b)^{1 / 2}left(a^{n-1}+b^{n-1}right) ) ( a^{n}+b^{n}=a^{n-1 / 2} cdot b^{1 / 2}+b^{n-1 / 2 cdot a^{1 / 2}} ) ( a^{n}-a^{n-1 / 2} b^{1 / 2}+b^{n}-b^{n-1 / 2} cdot a^{y} 2= ) ( a^{n}left[a mid-frac{b^{1 / 2}}{a^{1 / 2}}right]+b^{n}left[1-frac{a^{1 / 2}}{b^{4} n}right]^{20} ) ( a^{n-1}=left[a^{1 / 2}-b^{1 / 2}right]-b^{n-12} 2left[a^{11} 2-b^{1 / 2}right]=0 ) ( left[a^{1 / 2}-b^{4} 2right]left[a^{n-1 / 2}-b^{n-1 / 2}right]=0 ) ( frac{a^{n-1 / 2}}{b^{n-1 / 2}}=0 ) ( n=42 )
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