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SSC Selection Post 2019 PYQ — Question 58

SSC Selection Post - Graduation Level 2019 - 16 Oct 2019 • Quantitative Aptitude • Q58

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If x + y + z = 17 and xy + yz + zx = 85, then what is the value of (x3+y3+z3−3xyz)\sqrt{(x ^ 3 + y ^ 3 + z ^ 3 - 3xyz)} ?
 

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Correct answer: B

Explanation

The correct answer is Option 2 i.e. 17217\sqrt2.

x3+y3+z3−3xyz=(x+y+z)3−3(x+y+z)(xy+yz+zx)=173−3×17×85=4913−4335=578x3+y3+z3−3xyz=578=289×2=172x^3 + y^3 + z^3 - 3xyz = (x + y + z)^3 - 3(x + y + z)(xy + yz + zx) \\ = 17^3 - 3 \times 17 \times 85 = 4913 - 4335 = 578 \\ \sqrt{x^3 + y^3 + z^3 - 3xyz} = \sqrt{578} = \sqrt{289 \times2} = 17\sqrt{2}