If x+y+z = 7 x2 + y2 + z2 = 85 x3 + y3

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If x+y+z = 7

x² + y² + z² = 85

x³ + y³ + z³ = 913

then $\sqrt[3]{xyz}-4$ is equal to:

Options:

Correct Answer:

Explanation:

(x+y+z)² = x² + y² + z² + 2(xy +yz+zx)

49 = 85 + 2(xy +yz+zx)

xy +yz+zx = -18

x³ + y³ + z³ - 3xyz = (x+y+z) (x² + y² + z²- xy - yz - zx)

913 - 3xyz = (7)(85 -(-18))

3xyz = 192

xyz = 64

$\sqrt[3]{xyz}-4$ = $\sqrt[3]{64}-4$ = 0