Answer to Question #189473 in Math for Charles

Question #189473

If α+β are the roots of the equation 3x^2-5x+6=0. Find the value of α/β+β/α


1
Expert's answer
2021-05-07T14:15:04-0400

Let "\\alpha" and "\\beta" be roots of the equation "3x^2-5x+6=0" ,

Using Viet Theorem, we obtain that "\\alpha +\\beta =\\frac{5}{3}" and "\\alpha \\beta=\\frac{6}{3}=2" .


"\\frac{\\alpha}{\\beta}+\\frac{\\beta}{\\alpha}=\\frac{\\alpha^2+\\beta^2}{\\alpha\\beta}= \\frac{\\alpha^2+2\\alpha\\beta+\\beta^2-2\\alpha \\beta}{\\alpha\\beta}= \\frac{(\\alpha+\\beta)^2-2\\alpha \\beta}{\\alpha\\beta}=\\frac{\\left(\\frac{5}{3}\\right)^2-2\\cdot 2}{2}=\\frac{25-36}{18}=-\\frac{11}{18}"


Answer: "\\frac{\\alpha}{\\beta}+\\frac{\\beta}{\\alpha}=-\\frac{11}{18}" .


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Comments

Assignment Expert
10.05.21, 12:17

The term 2βα was added, later the term 2βα was subtracted because 0=2βα- 2βα.

Charles
08.05.21, 11:45

Where did you get the -2βα from

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