In the following question, one or two equation(s) is/are given. You have to solve both the equations and find the relation between ‘x’ and ‘y’ and mark correct answer. I. 8x4

In the following question, one or two equation(s) is/are given. You have to solve both the equations and find the relation between ‘x’ and ‘y’ and mark correct answer.

I. 8x⁴ – 18x² + 4 = 0

II. 12y² + 29y + 14 = 0

A x > y

B x ≥ y

C x < y

D x ≤ y

E x = y or the relation cannot be determined

Solution

Correct Answer: Option E

We will solve both the equations separately.

Equation I:

8x⁴ – 18x² + 4 = 0

Let x² = a

⇒ 8a² –18a + 4 = 0

⇒ 8a² – 16a – 2a + 4 = 0

⇒ 8a(a – 2) – 2(a – 2) = 0

⇒ (8a - 2)(a - 2) = 0

⇒ a = ¼ or a = 2

Since x = √a

∴ x = ±½= ±0.5 or, x = √2 = ±1.41

Equation II:

12y² + 29y + 14 = 0

⇒ 12y² + 21y + 8y + 14 = 0

⇒ 3y(4y + 7) + 2(4y + 7) = 0

⇒ (3y + 2) (4y + 7) = 0

⇒ y = -2/3 = -0.67 or y = -7/4 = -1.75

Comparing the values of x and y, we get,

Few values of x are greater than y and few are smaller, same is true for y too. So, relation cannot be determined.

Solution

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