Cube root

Algebra Level 3

Let x = − 10 + 6 3 3 = − a + b c x=\sqrt [ 3 ]{ -10+6\sqrt{3} } =-a+b\sqrt{c} , where a a , b b and c c are positive integers. Find a + b + c a+b+c .


The answer is 5.

Alan Enrique Ontiveros Salazar by Alan Enrique Ontiveros S… , 22

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4 solutions

Aaditya Dhull
Feb 27, 2014

cubing both sides one can solve thereafter after compairing real with real part and radicals with radicals c=3,a=b=1

2 Helpful 0 Interesting 0 Brilliant 0 Confused

how? can show it step by step?

Andrew YoonHang - 7 years, 1 month ago
Nikky Fauzdar
Mar 1, 2014

take cube on both sides and comparing radical and rational partwe get c=3 a^3+9ab^2=10 and b^3+ba^2=2 and it is given a,b,c are positve integers it is possible when a=1 b=1

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ramiel To-ong
Feb 2, 2016

logical thinking

0 Helpful 0 Interesting 0 Brilliant 0 Confused

The cuberoot(6sqrt(3)-10) = sqrt(3)-1. Thus, 1+1+3 =5

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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