In the opening pages of the feminine mystique, betty friedan wrote about a problem that "lay buried, unspoken, for many years in the minds of american women." what was this problem?

That women were unfulfilled and unhappy in the limited role American society assigned to them.

Betty Friedan was an early leader of the feminist movement in the United States.  Her important book, The Feminine Mystique, published in 1963, argued that women in America were being misled into an unfulfilling and unhappy way of life.  They were made to believe that fulfillment and happiness as a woman came from being a wife, mother, homemaker.  But Friedan's studies of women showed that women were not happy just from that, that they were hungering for something else.  Their whole identity was coming from their roles or relationships to others in the home, not from who they actually were themselves.
Friedan's book challenged the existing patterns that existed in American society and pushed for women to have more of their own value for their own sake.  As she said (in chapter one):  "We can no longer ignore the voice within women that says, 'I want something more than my husband and my children and my home.'"

The answer to that question is a