Instructions

In each of the following questions, two equations I and II have been given. Solve these questions and answer

(1)if x < y
(2) if x ≤ y
(3) if x = y or the relation cannot be established
(4) if ≥ y
(5) if x > y

Question 25

I.$$9x^{2}+3x-2=0$$
II.$$8y^{2}+6y+1=0$$

Solution

Statement I : $$9x^{2}+3x-2=0$$

=> $$9x^2 + 6x - 3x - 2 = 0$$

=> $$3x (3x + 2) - 1 (3x + 2) = 0$$

=> $$(3x - 1) (3x + 2) = 0$$

=> $$x = \frac{1}{3} , \frac{-2}{3}$$

Statement II : $$8y^{2}+6y+1=0$$

=> $$8y^2 + 4y + 2y + 1 = 0$$

=> $$4y (2y + 1) + 1 (2y + 1) = 0$$

=> $$(4y + 1) (2y + 1) = 0$$

=> $$y = \frac{-1}{4} , \frac{-1}{2}$$

$$\therefore$$ No relation can be established.

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I.$$9x^{2}+3x-2=0$$II.$$8y^{2}+6y+1=0$$