The golden number frac{1+sqrt{5}}{2} is one o | vedclass

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

Question

(C) Let $x = \frac{1+\sqrt{5}}{2}$.Multiply both sides by $2$: $2x = 1+\sqrt{5}$.Subtract $1$ from both sides: $2x-1 = \sqrt{5}$.Square both sides: $(

Vedclass · Accepted Answer

$x^{2}-x-1=0$

Vedclass · Answer

(C) Let $x = \frac{1+\sqrt{5}}{2}$.Multiply both sides by $2$: $2x = 1+\sqrt{5}$.Subtract $1$ from both sides: $2x-1 = \sqrt{5}$.Square both sides: $(2x-1)^{2} = (\sqrt{5})^{2}$.Expand the left side: $4x^{2}-4x+1 = 5$.Rearrange the terms: $4x^{2}-4x-4 = 0$.Divide the entire equation by $4$: $x^{2}-x-1 = 0$.Thus,the golden number is a root of the quadratic equation $x^{2}-x-1=0$.

The golden number $\frac{1+\sqrt{5}}{2}$ is one of the solutions of ...... .

Similar Questions

Find the roots of the following quadratic equation by the method of completing the square: $3 y^{2}+7 y-20=0$

If both the roots of $25x^{2} - x(m - 2) - 1 = 0$ are opposite,then $m = \ldots$

$x=2$ is a solution of the equation $\ldots \ldots \ldots \ldots.$

Obtain the roots of the following quadratic equation by using the quadratic formula: $9x^{2} + 7x - 2 = 0$.

Solve the following quadratic equation using the quadratic formula,if the equation has a solution in $R$: $48m^{2} - 13m - 1 = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module