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Three positive numbers a,b,c are in A.P prove that `1/(sqrtb+sqrtc)`,`1/(sqrtc+sqrta)`and `1/(sqrta+sqrtb)`are aslo in A.P

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Three positive numbers a, b, c are in A.P. Prove that (1)/(sqrt(b)+sqrt(c )), (1)/(sqrt(c )+sqrt(a)) , (1)/(sqrt(a) + sqrt(b)) are also in A.P.

If a^(2), b^(2), c^(2) are in A.P., prove that (1)/(b+c), (1)/(c+a), (1)/(a+b) are also in A.P.

If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a),1/(a-b) are also in A.P.

If a, b, c are in H.P., prove that, a(b+c), b(c+a), c(a+b) are in A.P.

If a^2, b^2, c^2 are in A.P , then prove that 1/(b+c), 1/(c+a),1/(a+b) are in A.P

If four positive numbers a, b, c and d are in A.P. then prove that abc, abd, acd and bcd are in H.P.

If (b-c)^(2), (c-a)^(2), (a-b)^(2) are in A.P. then prove that, (1)/(b-c), (1)/(c-a), (1)/(a-b) are also in A.P.

If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+(1//a c),c+1//(a b) are also in A.P.

If a, b, c are in A.P. then show that, a((1)/(b)+(1)/(c )), b((1)/(c )+(1)/(a)) and c((1)/(a)+(1)/(b)) are also in A.P.

If a ,b ,c are in A.P., then prove that the following are also in A.P. 1/(sqrt(b)+sqrt(c)),1/(sqrt(c)+sqrt(a)),1/(sqrt(a)+sqrt(b))

UNITED BOOK HOUSE-HARE SCHOOL-EXERCISE
  1. Show that the equation of straight line xcosalpha+ysinalpha=p can be e...

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  2. If G is the G.M between two positive numbers a and b.show that 1/(G^2-...

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  3. Three positive numbers a,b,c are in A.P prove that 1/(sqrtb+sqrtc),1/(...

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  4. If a1,a2,a3,...,aaare in A.P then show that 1/(a1a2)+1/(a2a3)+1/(a3a4)...

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  5. If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal ,show...

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  6. Solve :barz=iz^2(z being a complex number)

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  7. if alpha,beta,gamma are in A>P show that cot=(sinalpha-singamma)/(cosg...

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  8. Prove that (1)/(2sin10^(@))-2sin70^(@)=1.

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  9. Prove that 0le3costheta+4sintheta+5le10

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  10. Show that 4(cos^3 10^@+sin^3 20^@)=3(cos10^@+sin20^@)

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  11. If the equation x^2-cx+d=0and x^2-ax+b=0 have a common root,and the ro...

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  12. If alphaand betaare roots of the equation qx^2+px+p=0,show that sqrt(a...

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  13. If z1 and z2 be two complex numbers show that Re(barz1z2)=1/2(z1barz2+...

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  14. Find the sum up to n terms :1+2/3+3/3^2+4/3^3+...

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  15. If x^(1/a)=y^(1/b)=z^(1/c)where a,b,c are in A.P,,than show that x,y,z...

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  16. If (acosthetasecphi-x)/(asin(theta+phi))=(y-bsinthetasecphi)/(bcos(th...

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  17. IF A+B+C=pi,then prove that tan (A/2)tan(B/2)+tan(B/2)tan(C/2)+tan(C/2...

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  18. Prove that secx=2/(sqrt(2+sqrt(2+sqrt(2+2cos8x)))

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  19. Prove that tan20^@+4sin20^@=sqrt3

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  20. A(1,2)and B(5,-2)are two points. P is a point moving in such a way tha...

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