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

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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 ...... .

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