If x + y + z = 19, xyz = 216 and xy + yz + zx = 114, then the value of √(x³+y³+z³+xyz) is :

If x + y + z = 19, xyz = 216 and xy + yz + zx = 114, then…

If x + y + z = 19, xyz = 216 and xy + yz + zx = 114, then the value of $\sqrt{x^3+y^3+z^3+xyz}$ is :

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 35.

We know that,

x³ + y³ + z³ = (x + y + z)[(x+ y + z)² - 3(xy + yz + zx) + 3xyz

According to the question

We have-

⇒ √(x³ + y³ + z³ + xyz)

⇒ √[(x + y + z){(x + y + z)² - 3(xy + yz + zx)} + 3xyz + xyz]

⇒ √(19 × (192 - 3 × 114) + 4 × 216)

⇒ √(19(361 - 342) + 864)

⇒ √(19 × 19 + 864)

⇒ √(1225) = 35

The value of $\sqrt{x^3+y^3+z^3+xyz}$ = 35