Solve the quadratic equation. 9) 9x2 - 4 = 0?
回答 (9)
2009-07-05 4:57 pm
✔ 最佳答案
Very basic. Do not forget the ±9x² = 4
x² = 4/9
x = ±√(4/9) = ± 2/3
You can also do by factoring, but only because both numbers are squares. If even one of them were not, you would need to use this technique.
2009-07-05 4:55 pm
Difference of two squares: a^2 - b^2 = (a + b)(a - b)
9x^2 - 4 = 0 (factor as difference of two squares)
(3x + 2)(3x - 2) = 0 (zero-product property)
3x + 2 = 0 or 3x - 2 = 0
3x = -2 or 3x = 2
x = -2/3 or x = 2/3 <===ANSWER
or you could solve it this way
9x^2 - 4 = 0 (add 4 to both sides)
9x^2 = 4 (divide both sides by 9)
x^2 = 4/9 (square root both sides)
x = +/- 2/3 <===ANSWER
9x^2 - 4 = 0 (factor as difference of two squares)
(3x + 2)(3x - 2) = 0 (zero-product property)
3x + 2 = 0 or 3x - 2 = 0
3x = -2 or 3x = 2
x = -2/3 or x = 2/3 <===ANSWER
or you could solve it this way
9x^2 - 4 = 0 (add 4 to both sides)
9x^2 = 4 (divide both sides by 9)
x^2 = 4/9 (square root both sides)
x = +/- 2/3 <===ANSWER
2009-07-05 4:55 pm
2/3 or -2/3
2015-08-17 4:36 am
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Solve the quadratic equation. 9) 9x2 - 4 = 0?
RE:
Solve the quadratic equation. 9) 9x2 - 4 = 0?
參考: solve quadratic equation 9 9x2 4 0: https://shortly.im/tPKGS
2009-07-09 8:08 am
9x^2 = 4
x^2 = 4/9
x = ± (2/3)
x^2 = 4/9
x = ± (2/3)
2009-07-05 5:16 pm
a^2 - b^2 ≡ (a + b)(a - b)
9x^2 - 4 = 0
(3x)^2 - 2^2 = 0
(3x + 2)(3x - 2) = 0
3x + 2 = 0
3x = -2
x = -2/3
3x - 2 = 0
3x = 2
x = 2/3
∴ x = ±2/3
9x^2 - 4 = 0
(3x)^2 - 2^2 = 0
(3x + 2)(3x - 2) = 0
3x + 2 = 0
3x = -2
x = -2/3
3x - 2 = 0
3x = 2
x = 2/3
∴ x = ±2/3
2009-07-05 5:07 pm
Add 4 to both sides:
9x^2=4
Divide both sides by 9:
x^2=4/9
Take the square root of both sides:
x= +/- 2/3 so x=2/3 or x= -2/3 (answer)
You could do this by using the quadratic formula if you wanted. Refer to my Math Variety blog post on how to solve quadratic equations by using the quadratic formula. I have an explanation of what the quadratic formula is, practice problems, and solutions.
http://mathvariety.blogspot.com/2009/04/solving-quadratic-equations-by-using.html
http://mathvariety.blogspot.com/2009/05/solving-quadratic-equations-by-using.html
http://mathvariety.blogspot.com/2009/05/solving-quadratic-equations-by-using_24.html
Check out my eHow article on how to solve quadratic equations by using the quadratic formula:
http://www.ehow.com/how_4816180_quadratic-equation-using-quadratic-formula.html
Also check out this link. It’s a calculator that will give you the roots (solutions) to any quadratic equation. Just enter values for a, b, and c.
http://www.1728.com/quadratc.htm
The quadratic formula is:
x = [-b +/- sqrt(b^2-4ac)]/(2a)
9x^2=4
Divide both sides by 9:
x^2=4/9
Take the square root of both sides:
x= +/- 2/3 so x=2/3 or x= -2/3 (answer)
You could do this by using the quadratic formula if you wanted. Refer to my Math Variety blog post on how to solve quadratic equations by using the quadratic formula. I have an explanation of what the quadratic formula is, practice problems, and solutions.
http://mathvariety.blogspot.com/2009/04/solving-quadratic-equations-by-using.html
http://mathvariety.blogspot.com/2009/05/solving-quadratic-equations-by-using.html
http://mathvariety.blogspot.com/2009/05/solving-quadratic-equations-by-using_24.html
Check out my eHow article on how to solve quadratic equations by using the quadratic formula:
http://www.ehow.com/how_4816180_quadratic-equation-using-quadratic-formula.html
Also check out this link. It’s a calculator that will give you the roots (solutions) to any quadratic equation. Just enter values for a, b, and c.
http://www.1728.com/quadratc.htm
The quadratic formula is:
x = [-b +/- sqrt(b^2-4ac)]/(2a)
2009-07-05 4:57 pm
This is the difference of squares.
9x² - 4 = (3x)² - (2)²
= (3x+2)(3x-2)
x = ±2/3
9x² - 4 = (3x)² - (2)²
= (3x+2)(3x-2)
x = ±2/3
2009-07-05 4:54 pm
x^2 = 4/9
x = +/- 2/3
x = +/- 2/3
2009-07-05 4:54 pm
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