Keep it short please

Algebra Level 2

If x = 7 1 x=\sqrt{7}-1 , find the value of 3 x 3 + 12 x 2 6 x 12 3x^{3}+12x^{2}-6x-12 .


The answer is 24.

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1 solution

Chew-Seong Cheong
Feb 16, 2015

If x = 7 1 x 2 + 2 x 6 = 0 x = \sqrt{7} - 1\quad \Rightarrow x^2 + 2x - 6 = 0

3 x 3 + 12 x 2 6 x 12 = 3 x 3 + 12 x 2 6 x 36 + 24 = ( x 2 + 2 x 6 ) ( 3 x + 6 ) + 24 = 0 + 24 = 24 \begin{aligned} 3x^3+12x^2-6x-12 & = 3x^3+12x^2-6x-36+24 \\ & = (x^2 + 2x - 6)(3x+6)+24 \\ & = 0 + 24 \\ & = \boxed{24} \end{aligned}

great..! how do u thought of it

Aman Gautam - 6 years, 3 months ago

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He transposed the 1 on the RHS to LHS and squared both sides. (y) Chew!

Hem Shailabh Sahu - 6 years, 3 months ago

exactly how I solved this problem

Qian Yu Hang - 6 years, 3 months ago

can't we first factorize the first eq and put the result into the second eq

Prakhar Dhumas - 6 years, 3 months ago

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