Prove that the roots of the equation (b + c – 2a)x² + (c + a – 2b)x + (a + b – 2c) = 0 are rational.

Ateacher wanted to buy a chair, a bookshelf, two tables and a desk. she spent $900 for all five items and the chair and the desk combined 70% of her total. if the bookshelf cost $50, how much did each of the tables cost?