Grade 12th passAlgebra
If G is the G.M between two positive numbers a and b, show that1/G²-a²+1/G²-b²=1/G².
2 Answers
Arun
Approved Tutor Answer8 Years agoDear student
G is the G.M. between a & b.
G² = ab
Then LHS
1/(G²- a²) + 1/(G²-b²)
= 1/ab- a² + 1/ab - b²
= 1/a(b-a) - 1/b(b-a)
= (b -a)/ (ab) *(b-a)
= 1/ab
= 1/G²
= RHS
Hence proved.
Regards
Arun (askIITians forum expert)
Sneha Khanal
If A be the arithmetic vmean and H, the H.M between two quantities a and b, show that a-A/a-H * b-A/b-H = A/H
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