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LekaFEV [45]
2 years ago
13

Which equation has the solutions x=1+or-square root of 5?

Mathematics
2 answers:
stiv31 [10]2 years ago
5 0

We will proceed to solve each case to determine the solution of the problem.

<u>case a)</u> x^{2}+2x+4=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

x^{2}+2x=-4

Complete the square. Remember to balance the equation by adding the same constants to each side.

x^{2}+2x+1=-4+1

x^{2}+2x+1=-3

Rewrite as perfect squares

(x+1)^{2}=-3

(x+1)=(+/-)\sqrt{-3}\\(x+1)=(+/-)\sqrt{3}i\\x=-1(+/-)\sqrt{3}i

therefore

case a) is not the solution of the problem

<u>case b)</u> x^{2}-2x+4=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

x^{2}-2x=-4

Complete the square. Remember to balance the equation by adding the same constants to each side.

x^{2}-2x+1=-4+1

x^{2}-2x+1=-3

Rewrite as perfect squares

(x-1)^{2}=-3

(x-1)=(+/-)\sqrt{-3}\\(x-1)=(+/-)\sqrt{3}i\\x=1(+/-)\sqrt{3}i

therefore

case b) is not the solution of the problem

<u>case c)</u> x^{2}+2x-4=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

x^{2}+2x=4

Complete the square. Remember to balance the equation by adding the same constants to each side.

x^{2}+2x+1=4+1

x^{2}+2x+1=5

Rewrite as perfect squares

(x+1)^{2}=5

(x+1)=(+/-)\sqrt{5}\\x=-1(+/-)\sqrt{5}

therefore

case c) is not the solution of the problem

<u>case d)</u> x^{2}-2x-4=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

x^{2}-2x=4

Complete the square. Remember to balance the equation by adding the same constants to each side.

x^{2}-2x+1=4+1

x^{2}-2x+1=5

Rewrite as perfect squares

(x-1)^{2}=5

(x-1)=(+/-)\sqrt{5}\\x=1(+/-)\sqrt{5}

therefore

case d) is the solution of the problem

therefore

<u>the answer is</u>

x^{2}-2x-4=0

vekshin12 years ago
5 0
D. x^2 - 2x - 4 = 0.....using the quadratic formula, the result will be :
x = 1 (+-) sqrt 5
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