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x,y are two real numbers. If A is half o...

x,y are two real numbers. If A is half of their sum, G is root of their product and H is average of their reciprocls then

A

A.H = `G^(2)`

B

G = A.H

C

A = `HG^(2)`

D

A = G + H

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-SEQUENCES AND SERIES -EXERCISE
  1. If the geometic mean between a and b is (a^(n + 1) + b^(n + 1))/(a^(n)...

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  2. If the harmonic mean between a and b is (a^(n + 1) + b^(n - 1))/(a^(n)...

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  3. x,y are two real numbers. If A is half of their sum, G is root of thei...

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  4. If the first and (2n + 1)th terms of an A.P. , G.P. and H.P. are equal...

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  5. If H(1), H(2), ….. H(n) are n harmonic means between a and b (ne a), t...

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  6. The harmonic mean of two numbers is 4 their arithmetic mean is A and g...

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  7. The ratio of the harmonic mean to the geometric mean of two positive n...

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  8. If b + c, c + a , a + b are in A.P then a , b , c are in

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  9. If a^(2), b^(2), c^(2) are in A.P., then (a)/(b + c) , (b)/(c + a), (c...

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  10. IF the roots of (b-c) x^2+ (c-a) x+ (a-b) =0 are equal then ...

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  11. IF the roots of a(b-c)x^2+b (c-a) x+c (a-b)=0 are equal then a, ...

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  12. If the sum of the roots of the quadratic equation ax^(2) + bx + c = 0 ...

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  13. If the system of linear equations x+2ay+az=0, x+3by+bz=0,x+4ch+cz=0 ha...

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  14. Let f (x ) be a polynomial function of second degree. If f (1) = f( -1...

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  15. If x gt 1, y gt 1 , z gt 1 are in G.P then (1)/(1 + log x ), (1)/( 1...

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  16. If (a + bx)/(a - bx) = (b + cx)/(b - cx) = (c + dx)/(c - dx)( x ne 0),...

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  17. If a^(x) = b^(y) = c^(z) = d^(t) and a ,b ,c d are in G.P . Then x, y,...

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  18. If a,b and c are in G.P then (b - a)/(b - c) + (b + a)/(b + c)

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  19. If a,b,c are unequal numbers such that a,b,c are in A.P and b - a, c -...

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  20. If 2(y - a) is the H.M between y - x and y - z, then x - a, y -a, z - ...

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