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# help

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If a and b are the roots of x^2 - 4x + 1 = 0, find a^3 + b^3.

Dec 17, 2019

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If a and b are the roots of x^2 - 4x + 1 = 0, find a^3 + b^3.

Hello Guest!

$$\{a,b \}\subseteq\{x_1,x_2 \}$$

$$x^2 - 4x + 1 = 0\\ x=2\pm \sqrt{4-1}\\ x_1=2+\sqrt{3}\\ x_2=2-\sqrt{3}$$

$$a^3+b^3=(2+\sqrt{3})^3+(2-\sqrt{3})^3=26+15\sqrt{3}+26-15\sqrt{3}$$

$$a^3+b^3=52$$

!

Dec 17, 2019