Instructions

In each of the following questions, two equations numbered I and II are given. You have to solve both the equations and select the appropriate option.
Give answer If
a: x > y
b: x ≤ y
c: x ≥ y
d: x < y
e: Relationship between x and y cannot be established

Question 63

I. $$2x^{2}-15x+27=0$$
II. $$2y^{2}-23y+63=0$$

Solution

I.$$2x^{2} - 15x + 27 = 0$$

=> $$2x^2 - 6x - 9x + 27 = 0$$

=> $$2x (x - 3) - 9 (x - 3) = 0$$

=> $$(x - 3) (2x - 9) = 0$$

=> $$x = 3 , \frac{9}{2}$$

II.$$2y^{2} - 23y + 63 = 0$$

=> $$2y^2 - 14y - 9y + 63 = 0$$

=> $$2y (y - 7) - 9 (y - 7) = 0$$

=> $$(y - 7) (2y - 9) = 0$$

=> $$y = 7 , \frac{9}{2}$$

$$\therefore x \leq y$$

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I. $$2x^{2}-15x+27=0$$II. $$2y^{2}-23y+63=0$$

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I. $$2x^{2}-15x+27=0$$
II. $$2y^{2}-23y+63=0$$