In this article, we prove that the double inequalities \t\t\tα1[7C(a,b)16+9H(a,b)16]+(1−α1)[3A(a,b)4+G(a,b)4]<E(a,b)<β1[7C(a,b)16+9H(a,b)16]+(1−β1)[3A(a,b)4+G(a,b)4],[7C(a,b)16+9H(a,b)16]α2[3A(a,b)4+G(a,b)4]1−α2<E(a,b)<[7C(a,b)16+9H(a,b)16]β2[3A(a,b)4+G(a,b)4]1−β2\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document} $$\\begin{aligned} &\\alpha_{1} \\biggl[\\frac{7C(a,b)}{16}+\\frac{9H(a,b)}{16} \\biggr]+(1- \\alpha_{1}) \\biggl[\\frac{3A(a,b)}{4}+\\frac{G(a, b)}{4} \\biggr]\\\\ &\\quad< E(a,b) \\\\ &\\quad< \\beta_{1} \\biggl[\\frac{7C(a,b)}{16}+\\frac{9H(a,b)}{16} \\biggr]+(1- \\beta_{1}) \\biggl[\\frac{3A(a,b)}{4}+\\frac{G(a, b)}{4} \\biggr], \\\\ &\\biggl[\\frac{7C(a,b)}{16}+\\frac{9H(a,b)}{16} \\biggr]^{\\alpha _{2}} \\biggl[ \\frac{3A(a,b)}{4}+\\frac{G(a, b)}{4} \\biggr]^{1-\\alpha_{2}}\\\\ &\\quad< E(a,b) \\\\ &\\quad< \\biggl[\\frac{7C(a,b)}{16}+\\frac{9H(a,b)}{16} \\biggr]^{\\beta _{2}} \\biggl[ \\frac{3A(a,b)}{4}+\\frac{G(a, b)}{4} \\biggr]^{1-\\beta_{2}} \\end{aligned}$$ \\end{document} hold for all a, b>0 with aneq b if and only if alpha_{1}leq 3/16=0.1875, beta_{1}geq64/pi^{2}-6= 0.484555dots, alpha_{2}leq3/16=0.1875 and beta_{2}geq(5log2-log3-2log pi)/(log7-log6)= 0.503817dots, where E(a,b)= (frac{2}{pi}int^{pi/2}_{0}sqrt{acos^{2}theta +bsin^{2}theta},dtheta )^{2}, H(a,b)=2ab/(a+b), G(a,b)=sqrt{ab}, A(a,b)=(a+b)/2 and C(a,b)=(a^{2}+b^{2})/(a+b) are the quasi-arithmetic, harmonic, geometric, arithmetic and contra-harmonic means of a and b, respectively.