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The product of three and a squared number is twice the sum of the number and four

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asked Feb 20, 2015 90.8k views

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The product of three and a squared number is twice the sum of the number and four

Mathematics
high-school

Hung Tran asked

by Hung Tran

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2 Answers

4 votes

$3x^2=2(x+4)\\ 3x^2=2x+8\\ 3x^2-2x-8=0\\ 3x^2-6x+4x-8=0\\ 3x(x-2)+4(x-2)=0\\ (3x+4)(x-2)=0\\ x=-(4)/(3) \vee x=2$

NPNelson answered Feb 21, 2015

by NPNelson

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3 votes

From the text of the task we can write the equation:

$3 x^(2) =2(x+4)\\ \\ 3x^2=2x+8\\ \\ 3x^2-2x-8=0\\ \\ \Delta=(-2)^2-4.3.(-8)=4+96=100\\ \\ x=(2 \pm√(100))/(2.3)=(2 \pm10)/(6)\\ \\ x_1=(2-10)/(6)=-(8)/(6)=-(4)/(3)\\ \\ x_2=(2+10)/(2.3)=(12)/(6)=2$

Erickthered answered Feb 24, 2015