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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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?

Similar Questions

Check whether the following is a quadratic equation:
$x^{2}+3x+1=(x-2)^{2}$

We get $2$ litres of kerosene less in Rs. $360$ if the price of kerosene increases by Rs. $2$ per litre. Find the original price of kerosene per litre.

$A$ car takes $60$ minutes less for a journey of $150\,km$,if its speed is increased by $5\,km/hr$ from its usual speed. Find the original speed of the car in $km/hr$.

Examine whether the following equation is quadratic or not: $3x^{2} + 5\sqrt{x} + 3 = 0$.

If one of the roots of the equation $px^{2} + qx + r = 0$ where $p \neq 0$ and $p, q, r \in R$ is $x = -2$,then prove that $4p - 2q + r = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module