The golden ratio,often denoted by the Greek l | vedclass

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Question

(B) The golden ratio,denoted by $\phi$,is defined as the ratio of two quantities such that the ratio of the sum of the quantities to the larger quanti

Vedclass · Accepted Answer

$\frac{1+\sqrt{5}}{2}$

Vedclass · Answer

(B) The golden ratio,denoted by $\phi$,is defined as the ratio of two quantities such that the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.Mathematically,for two quantities $a$ and $b$ where $a > b > 0$,the golden ratio is defined as $\frac{a+b}{a} = \frac{a}{b} = \phi$.This leads to the quadratic equation $\phi^2 - \phi - 1 = 0$.Using the quadratic formula $\phi = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$,we get $\phi = \frac{1 \pm \sqrt{1 - 4(1)(-1)}}{2(1)} = \frac{1 \pm \sqrt{5}}{2}$.Since the ratio must be positive,we take the positive root: $\phi = \frac{1+\sqrt{5}}{2} \approx 1.618$.

The golden ratio,often denoted by the Greek letter $\phi$,is a special number. Which of the following is the golden number?

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