An algebra problem by Wildan Bagus Wicaksono

Algebra Level 1

If x = 11 − 1 3 x=\dfrac { \sqrt { 11 } -1}3 , find 9 x 2 + 6 x + 2017 9{ x }^{ 2 }+6x+2017 .


The answer is 2027.

Wildan Bagus Wicaksono by Wildan Bagus Wicaksono , 18, Indonesia

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1 solution

x = 1 3 ( 11 − 1 ) 3 x = 11 − 1 3 x + 1 = 11 ( 3 x + 1 ) 2 = 11 9 x 2 + 6 x + 1 = 11 9 x 2 + 6 x + 2017 = 2027 \large x=\frac { 1 }{ 3 } \left( \sqrt { 11 } -1 \right) \\ \large 3x=\sqrt { 11 } -1\\ \large 3x+1=\sqrt { 11 } \\ \large { (3x+1) }^{ 2 }=11\\ \large { 9x }^{ 2 }+6x+1=11\\ \large { 9x }^{ 2 }+6x+2017=2027

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