Let P and Q be two points in xy−plane on the curve y=x7−2x5+5x3+8x+5 such that −−→OP⋅^i=2 and −−→OQ⋅^i=−2 and the magnitude of −−→OP+−−→OQ=2M (where O is origin). Then the value of M is

Let P and Q be two points in xy−plane on the curve y=x7−2x5+5x3+8x

1.	Let P and Q be two points in xy−plane on the curve y=x7−2x5+5x3+8x+5 such that −−→OP⋅^i=2 and −−→OQ⋅^i=−2 and the magnitude of −−→OP+−−→OQ=2M (where O is origin). Then the value of M is
Answer» Let $P$ and $Q$ be two points in $x y -$ plane on the curve $y = x^{7} - 2 x^{5} + 5 x^{3} + 8 x + 5$ such that $- - \to O P \cdot^i = 2$ and $- - \to O Q \cdot^i = - 2$ and the magnitude of $- - \to O P + - - \to O Q = 2 M$ $($ where $O$ is origin $) .$ Then the value of $M$ is