quadratic equations X2-4√3x+9=0
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Answered by
15
x^2 - 2.2√3.x +(2√3)^2 - (2√3)^2 +9 = 0
(x-2√3)^2 = (2√3)^2 - 9 = 12-9=3
x-2√3 = +√3, -√3
x= 2√3+√3, 2√3 -√3
x= 3√3, √3
(x-2√3)^2 = (2√3)^2 - 9 = 12-9=3
x-2√3 = +√3, -√3
x= 2√3+√3, 2√3 -√3
x= 3√3, √3
shaik6301927843:
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Answered by
20
The answer is given below :
The quadratic equation is
x² - 4√3 x + 9 = 0
If α and β are the roots of the given equation, then
α + β = - (- 4√3)/1 = 4√3
and
αβ = 9/1 = 9
To solve the problem,
x² - 4√3 x + 9 =0
⇒ x² - √3x - 3√3x + 9 = 0
⇒ x (x - √3) - 3√3 (x - √3) = 0
⇒ (x - √3) (x - 3√3) = 0
∴ the roots of the given quadratic equation are
x = √3, 3√3
[I hope it helps you.]
The quadratic equation is
x² - 4√3 x + 9 = 0
If α and β are the roots of the given equation, then
α + β = - (- 4√3)/1 = 4√3
and
αβ = 9/1 = 9
To solve the problem,
x² - 4√3 x + 9 =0
⇒ x² - √3x - 3√3x + 9 = 0
⇒ x (x - √3) - 3√3 (x - √3) = 0
⇒ (x - √3) (x - 3√3) = 0
∴ the roots of the given quadratic equation are
x = √3, 3√3
[I hope it helps you.]
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