Question

If x sq. y sq. = 4(xy - 1), then prove that x and y vary inversely as each other.​

Answer 1

Step-by-step explanation:

We have,

x²y² = 4(xy - 1)

Solving

x²y² = 4xy - 4

x²y² - 4xy + 4 = 0

(xy)² - 2(xy)(2) + (2)² = 0

We know that,

a² - 2ab + b² = (a - b)²

So,

(xy)² - 2(xy)(2) + (2)² = 0

(xy - 2)² = 0

(xy - 2) = √0

xy - 2 = 0

xy = 2

Since,

xy = A constant value,

x ∝ (1/y)

OR

xy = 2

x = 2/y

x = 2(1/y)

This can be written as,

x = k(1/y)

where k is a constant term and k = 2.

So,

x = k(1/y)

Then,

x ∝ (1/y)

Hence proved.

Hope it helped and believing you understood it. All the best.