Algebra.. :/

Algebra Level 3

Given: m^2 + m - 3 = 0,

What is the least possible value of: m^3 + 4m^2 + 2014 ?


The answer is 2023.

Christian Daang by Christian Daang , 20, Philippines

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2 solutions

Ariel Gershon
Oct 30, 2014

We have m 2 = − m + 3 m^2 = -m+3 . Hence m 3 = − m 2 + 3 m m^3 = -m^2+3m . Therefore, m 3 + 4 m 2 + 2014 = 3 m 2 + 3 m + 2014 = 3 ( − m + 3 ) + 3 m + 2014 = 2023 m^3+4m^2+2014 = 3m^2+3m+2014 = 3(-m+3)+3m+2014 = 2023

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Christian Daang
Oct 18, 2014

Given: m^2 + m - 3 = 0,

-----> m^2 = 3-m

------> m^2 + m = 3 Then,

m^3 + 4m^2 + 2014 = m(m^2) + 4(m^2) + 2014

= m(3-m) + 4(3-m) + 2014

= 3m-(m^2) + 12-4m + 2014

= -m-(m^2)+2026

= -(m+m^2) + 2026

= -(3) + 2026

= 2023

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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