The hypernetted-chain formalism for boson-boson mixtures described by an extended Jastrow correlated wave function is derived, taking into account elementary diagrams and triplet correlations. The energy of an ideal boson 3He-4He mixture is computed for low values of the 3He concentration. The zero-3He-concentration limit provides a 3He chemical potential in good agreement with the experimental value, when a McMillan two-body correlation factor and the Lennard-Jones potential are adopted. If the Euler equations for the two-body correlation factors are solved in presence of triplet correlations, the agreement is again improved. At the experimental 4He equilibrium density, the 3He chemical potential turns out to be -2.58 K, to be compared with the experimental value, -2.79 K.