Q2Please explain clearly, please solve correctly. Math real Analysis

(2) We used the inner product in a Hilbert space to define its norm. That leaves open the question of whether two different inner products could lead to the same norm. Show that that is not the case, by doing the following. (a) For a real Hilbert space, show that (x, y) = llac + yl12 - 1/2- 21/2) (b) For a complex Hilbert space, show that (x, y) = _ lla + yll2 + illa + zyll2 - lla - y|12 - illz - 23112)