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If A and G are the A.M.and G.M. of two unequal positive numbers a and b, show that `A>G>G^2/A`

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If A is the A.M. and G is the G.M. of two unequal positive real numbers p and q, prove that A gt G and |G| gt (G^(2))/(A)

If three equal positive numbes a,b,c are in G.P,then show that a+c>2b

The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that a:b =(m+sqrt(m^2-n^2)):(m-sqrt(m^(2)-n^2)) .

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If three unequal positive numbers a, b, c are in G.P. then show that, a +c gt 2b .

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If A.M and G.M of two positive real numbers are 25 and 15 respectively, then find their H.M.

If A.M. and G.M. of two positive numbers a and b are 10 and 8, respectively, find the numbers.

UNITED BOOK HOUSE-ALGEBRA-EXERCISE
  1. For any complex number z, show that the minimum value of | z| + | z -1...

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  2. If a=cosalpha+isinalphaand 1+sqrt(1-b^2)=nb,show that b/(2n)(1+na)(1+...

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  3. If x=a+bw+cw^2 ,show that x^3-3ax^2+3(a^2-bc)x=a^3+b^3+c^3-3abc.when w...

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  4. If one of the root of the equation (2 + 3i)x^2 - bx + (3 -i) = 0 is (2...

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  5. If w is an imaginary cube root of unity, show that w/9[(1-w)(1-w^2)(1-...

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  6. If p + q = m + n and p^2 + q^2 = m^2 + n^2, then by using mathematical...

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  7. If a. b, c are in G.P. and logca, logb c, loga b are in AP show that t...

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  8. If A and G are the A.M.and G.M. of two unequal positive numbers a and ...

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  9. In a G.P. 1st term and common ratio are a and r resp. and if th sum of...

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  10. If the sides of a triangle are three consecutive termsof a G.P. then s...

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  11. Show that : (^(4n)C(2n))/(^(2n)Cn) = (1.3.5...(4n-1))/{1.3.5...(2n-1)}...

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  12. For a le 0, determine all the roots of the equation x^2-2a |x-a|-3a^2 ...

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  13. Prove that nCr+3.nC(r-1)+3nC(r-2)+nC(r-3)=(n+3)Cr

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  14. If (1+x+x^2)^n=a0+a1x+a2x^2+....+a(2n)X^(2n),show that a0+a3+a6+.....=...

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  15. The coefficient of the term independent of x in the expansion of [((x+...

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  16. Prove that the inequations (2x+1)/(7x-1)>5and (x+7)/(x-8)>2have no sol...

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  17. How many five -digit numbers divisible by 3 can be formed using the di...

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  18. In how many cases there will be 3 Sundays when 20 dates are named at'r...

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