If (a + b + c) = 6 a2 + b2 + c2 = 32 a

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If (a + b + c) = 6

a² + b² + c² = 32

a³ + b³ + c³ = 189

find the value of abc + 3

Options:

Correct Answer:

Explanation:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

36 = a² + b² + c² + 2(ab + bc + ca)

36 = 32 + 2(ab + bc + ca)

ab + bc + ca = 2

Now → a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

189 – 3abc = 6(32 – 2)

abc = 3

abc + 3 = 6