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Suppose that 𝑎+1𝑏a+ b1​  and 𝑏+1𝑎b+ a1​  are the roots of the equation 𝑥2−𝑝𝑥+𝑞=0x 2 −px+q=0. If 𝑎𝑏=1ab=1, what is the value of 𝑞q?

Question

Suppose that 𝑎+1𝑏a+ b1​  and 𝑏+1𝑎b+ a1​  are the roots of the equation 𝑥2−𝑝𝑥+𝑞=0x 2 −px+q=0. If 𝑎𝑏=1ab=1, what is the value of 𝑞q?
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Solution 1

Dado que a+1b a + \frac{1}{b} y b+1a b + \frac{1}{a} son las raíces de la ecuación x2px+q=0 x^2 - px + q = 0 , y que ab=1 ab = 1 , vamos a encontrar el valor de q q .

Primero, recordemos que la suma de las raíces de la ecuación cuadrática x2px+q=0 x^2 - px + q = 0 es igual a p p , y el producto de Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.

Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
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