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. (x7/5 ÷ 9) = 169 ÷ x3/5 II. y1/4 × y1/4 × 7 = 273 ÷ y1/2

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. (x^7/5 ÷ 9) = 169 ÷ x^3/5

II. y^1/4 × y^1/4 × 7 = 273 ÷ y^1/2

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 D

We will solve both the equations separately.

Equation I:

(x^7/5 ÷ 9) = 169 ÷ x^3/5

\(\Rightarrow \frac{{{{(x)}^{\frac{7}{5}}}}}{9} = \frac{{169}}{{{x^{\frac{3}{5}}}}}\)

⇒ x^10/5 = 9 × 169

⇒ x² = 9 × 169

⇒ x = + (3 × 13), - (3 × 13)

⇒ x = +39 or – 39

Equation II:

y^1/4 × y^1/4 × 7 = 273 ÷ y^1/2

⇒ y^1/4 × y^1/4 × 7 = 273/y^1/2

⇒ y = 273/7 = 39

Comparing the values of x and y we get,

x ≤ y

Solution

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