In each of these questions two equations numbered I and II are given. You have to solve both the equations and –
Give answer a: if x < y
Give answer b: if x ≤ y
Give answer c: if x > y
Give answer d: if x ≥ y
Give answer e: if x = y or the relationship cannot be established.
I. $$x^{2}-15x+56=0$$
II. $$y^{2} -23y+132=0$$
I.$$x^{2} - 15x + 56 = 0$$
=> $$x^2 - 8x - 7x + 56 = 0$$
=> $$x (x - 8) - 7 (x - 8) = 0$$
=> $$(x - 8) (x - 7) = 0$$
=> $$x = 8 , 7$$
II.$$y^{2} - 23y + 132 = 0$$
=> $$y^2 - 11y - 12y + 132 = 0$$
=> $$y (y - 11) - 12 (y - 11) = 0$$
=> $$(y - 11) (y - 12) = 0$$
=> $$y = 11 , 12$$
$$\therefore x < y$$
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