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Pavlova-9 [17]
3 years ago
8

Solve:

Mathematics
2 answers:
STatiana [176]3 years ago
8 0

The solutions to the equation 3-k=\sqrt{3k+1} are k = 1 and 8

The given equation is:

3-k=\sqrt{3k+1}

Square both sides of the equation

(3-k)^2=3k+1

Expand the left side of the equation above

(3-k)^2=3k+1\\\\(3-k)(3-k)=3k+1\\\\3^2-3k-3k+k^2=3k+1\\\\9-6k+k^2=3k+1

Write the quadratic equation in standard form

k^2-6k-3k+9-1=0\\\\k^2-9k+8=0\\\\

Factor the quadratic equation

(k-8)(k-1)=0

Use the zero product property

k - 8 = 0

k = 8

k - 1 = 0

k = 1

The solutions to the equation 3-k=\sqrt{3k+1} are k = 1 and 8

Learn more here: brainly.com/question/25840704

IgorC [24]3 years ago
7 0

answer

first one: 8 and 1

second one: is 1

Step-by-step explanation:

slay

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The equation that fits the standard form of a Quadratic equation is 2(x + 5)² + 8x + 5 +  6 = 0 which can be re-written as 2x² + 28x + 61 = 0.

<h3>What is a Quadratic Equation?</h3>

Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown

From the given data, we check which of them fits the standard form of a quadratic equation.

  • 2(x + 5)² + 8x + 5+  6 = 0
  • x⁶ + 6x + 4  + 8 = 0
  • 7x⁶ + 36x³ + 5 = 0
  • 4x⁹ + 20x³ + 25 = 0

2(x + 5)² + 8x + 5 +  6 = 0

2( (x(x+5) + 5(x+5) ) + 8x + 5 +  6 = 0

2( x² + 5x + 5x + 25 ) + 8x + 5 +  6 = 0

2( x² + 10x + 25 ) + 8x + 5 +  6 = 0

2x² + 20x + 50 + 8x + 5 +  6 = 0

2x² + 20x + 8x + 50 + 5 +  6 = 0

2x² + 28x + 61 = 0

Therefore, the equation that fits the standard form of a Quadratic equation is 2(x + 5)² + 8x + 5 +  6 = 0 which can be re-written as 2x² + 28x + 61 = 0.

Learn more about quadratic equations here: brainly.com/question/1863222

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