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# If xy = 144, x + y = 30, and x > y. What is the value of x - y?

**Solution:**

(x-y)² = x² + y² - 2xy

Since xy = 144, we get

(x-y)² = x² + y² - 2(144) = x² + y² - 288 --------> (1)

We also know that

(x+y)² = x² + y² + 2xy = x² + y² + 288 ------->(2)

Now x + y = 30, hence substituting the value of x + y in equation (2) we get,

(30)² = x² + y² + 288

900 - 288 = x² + y²

x² + y² = 612 ------->(3)

Substituting (3) in (1)

(x-y)² = 612 - 288

(x-y)² = 324

x - y = √324 = 18

**Aliter**

Given, xy = 144 ---- (1)

and x + y = 30 ---- (2)

From equation (2), we get y = 30 - x

By substituting the value of y = 30 - x in equation (1), we get

⇒ x (30 - x) = 144

⇒ 30x - x^{2} = 144

⇒ x^{2 }- 30x + 144 = 0

We will factorize the quadratic equation by splitting the middle term.

⇒ x^{2 }- 24x - 6x + 144 = 0

⇒ x (x - 24) - 6(x - 24) = 0

⇒ (x - 6) (x - 24) = 0

⇒ x - 6 = 0 or x - 24 = 0

⇒ x = 6 or x = 24

It is given that x > y.

Therefore, x = 24 and y = 6.

⇒ x - y = 24 - 6 = 18

## If xy = 144, x + y = 30, and x > y. What is the value of x - y?

**Summary: **

Using the information provided in the problem statement the value of x - y thus obtained is 18.

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