If x + y = 12 and xy = 27, find the value of x³ + y³.

Solution:

Given, x + y = 12 and xy = 27

We have to find the value of x³ + y³.

Using the algebraic identity,

a³ + b³ = (a + b)(a² + b² - ab)

To find x² + y²

By using the algebraic identity,

(a + b)² = a² + 2ab + b²

(x + y)² = x² + 2xy + y²

(12)² = x² + 2(27) + y²

144 = x² + 54 + y²

x² + y² = 144 - 54

x² + y² = 90

Now, x³ + y³ = (x + y)(x² + y² - ab)

= (12)(90 - 27)

= 12(63)

= 756

Therefore, x³ + y³ = 756

✦ Try This: If x + y = 8 and xy = 12, find the value of x³ + y³.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

NCERT Exemplar Class 9 Maths Exercise 2.4 Sample Problem 1(i)

If x + y = 12 and xy = 27, find the value of x³ + y³

Summary:

If x + y = 12 and xy = 27, the value of x³ + y³ using the algebraic identity is 756

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