I just need the extraneous root

Mathematics

1 answer:

gregori [183]4 years ago

8 0

Answer:

Step-by-step explanation:

$2+\sqrt{2x-3} =\sqrt{x+7} ~~~(1)\\ x \ge -7\\and ~x\ge \frac{3}{2} \\squaring ~(1)\\4+2x-3+4\sqrt{2x-3} =x+7\\4\sqrt{2x-3} =x+7-2x-4+3\\4\sqrt{2x-1} =-x+6\\squaring\\16(2x-3)=x^2-12x+36\\32x-48=x^2-12x+36\\x^2-12x-32x+36+48=0\\x^2-44x+84=0\\\\x^2-2x-42x+84=0\\x(x-2)-42(x-2)=0\\(x-2)(x-42)=0\\x=2,42\\x=2 is a solution.\\whereas ~x=42 ~is~an~extraneous ~root.\\as~2+\sqrt{2*42-3} =\sqrt{42+7} \\2+\sqrt{81} =\sqrt{49} \\2+9=7\\or 11=7\\which~is~not~true.$

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The width of a golden rectangle is 15 feet. Find the perimeter of the rectangle to the nearest foot

Anika [276]

In a golden rectangle, the sides of the rectangle are as per the golden ratio. The perimeter of the golden rectangle with a width of 15 feet is 79 feet.

<h3>What is a golden rectangle?</h3>

In a golden rectangle, the sides of the rectangle are as per the golden ratio. The rectangle is given the name rectangle because of the fact that the ratio is the golden number 1.618.

In a golden rectangle, the sides of the rectangle are as per the golden ratio. Since the width of the rectangle is 15 feet, therefore, the length of the rectangle will be 1.618 times the width,

Length of the rectangle = 1.618 × 15 feet = 24.27 feet

Now, the perimeter of the rectangle can be written as,

$\rm \text{Perimeter of the rectangle} = 2(Length+ Width) \\\\\text{Perimeter of the rectangle} = 2(24.27+15)\\\\\text{Perimeter of the rectangle} = 78.54 \approx 79\ feet$