If x + 2y = 19 and $x^3 + 8y^3 = 361,$ t

CUET Preparation Today

Start Free Mocks

Home Questions D9QZ3A5UCS

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If x + 2y = 19 and $x^3 + 8y^3 = 361,$ then xy is equal to :

Options:

Correct Answer:

Explanation:

We know that,

(a + b)³ = a³ + b³ + 3ab(a + b)

Given,

x + 2y = 19

x³ + 8y³ = 361

According to the question,

(x + 2y)³ = x³ + 8y³ + 6xy(x + 2y)

= (19)³ = 361 + 6xy × 19

= 6859 = 361 + 114xy

= 114xy = (6859 – 361)

= 114xy = 6498

= xy = 57