- x + y + z
- 1
- 5
- (x + y + z)
^{2/3}

Option 2 : 1

**Given:**

x^{3} = y^{2} + z^{2 }, y^{3} = x^{2} + z^{2} and z^{3} = x^{2} + y^{2}

**Calculations:**

1/(1 + x) + 1/(1 + y) + 1/(1 + z)

Divide and multiply the equation by x^{2} in 1/(1 + x), y^{2} in 1/(1 + y) and z^{2} in 1/(1 + z)

⇒ x^{2}/(x^{2} + x^{3}) + y^{2}/(y^{2} + y^{3}) + z^{2}/(z^{2} + z^{3})

⇒ x^{2}/(x^{2} + y^{2 }+ z^{2}) + y^{2}/(y^{2} + x^{2} + z^{2}) + z^{2}/(z^{2} + y^{2} + x^{2})

⇒ (x^{2} + y^{2} + z^{2})/(x^{2} + y^{2} + z^{2})

⇒ 1

Now

⇒ 1^{1/3 } = 1

**∴**** The correct answer is option 2.**

India’s **#1 Learning** Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Trusted by 2,19,79,339+ Students

Testbook Edu Solutions Pvt. Ltd.

1st & 2nd Floor, Zion Building,

Plot No. 273, Sector 10, Kharghar,

Navi Mumbai - 410210

[email protected]
Plot No. 273, Sector 10, Kharghar,

Navi Mumbai - 410210

Toll Free:1800 833 0800

Office Hours: 10 AM to 7 PM (all 7 days)