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svet-max [94.6K]
3 years ago
6

What are the solutions to the equation x2 = 9? Explain why is more than one solution to the equation.

Mathematics
1 answer:
Firdavs [7]3 years ago
6 0

ANSWER

x =  - 3 \:  \: or \:  \: x = 3

The degree is two so it must have more than one solution.

EXPLANATION

The given equation is

{x}^{2}  = 9

Let us use the square root method to solve this equation.

Since the degree of x is two, the <em>fundamental theorem of algebra</em> says it must have 2 roots.

We take square root to obtain,

x =  \pm \sqrt{9}

x =  \pm3

Split the plus or minus sign to obtain,

x =  - 3 \:  \: or \:  \: x = 3

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What are the square roots of; (note: i think there are supposed to be 2 each) 36 12 1.96 0.64 400 25/36
Goryan [66]

Answer:

36 : 6 and -6

12 = 2\sqrt{3} ,  -2\sqrt{3}

1.96 =1.4 and -1.4

0.64 : 0.8 and -0.8

400 : 20 and -20

25/36 = 5/6 and -5/6

Step-by-step explanation:

we know that

(-x)^2 = x^2

ALSO

(x)^2 = x^2

thus, square of both negative and positive number is same positive number.

_________________________________________________

36 = 6*6

36 = -6*-6

hence

square roots of 36 is both -6 and 6

12 = 4*3 = 2^2*\sqrt{3} *\sqrt{3}

\sqrt{12} = 2\sqrt{3}

also

12 = -2\sqrt{3} *-2\sqrt{3}

\sqrt{12} = -2\sqrt{3}

___________________________________

1.96 = 196/100 = (14/10)^2

1.96 = 196/100 = (-14/10)^2

hence

\sqrt{1.96}  = 14/10  \ or -14/10

_______________________________

0.64 = 64/100 = (8/10)^2 = 0.8^2

0.64 = 64/100 = (-8/10)^2 = (-0.8)^2

Thus, square root of  0.64 = 0.8 and -0.8

_________________________________

400 = 20^2

400 = (-20)^2

\sqrt{400}  = 20\\\sqrt{400}  = -20\\

__________________________________

25/36 = (5/6)^2

25/36 = (-5/6)^2

\sqrt{ 25/36} = 5/6 \\\sqrt{ 25/36} = (-5/6

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Answer:

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Step-by-step explanation:

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