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Quadratic Equations
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30/05/2021 11:12 am
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Find the roots of the following equations:
(i) x-1/x = 3, x ≠ 0
(ii) 1/x+4 – 1/x-7 = 11/30, x = -4, 7
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30/05/2021 11:17 am
(i) x-1/x = 3
⇒ x2 – 3x -1 = 0
On comparing the given equation with ax2 + bx + c = 0, we get
a = 1, b = -3 and c = -1
By using quadratic formula, we get,
x = \(\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
x = \(\frac{3 \pm \sqrt{9 + 4}}{2}\)
x = \(\frac{3 \pm \sqrt{13}}{2}\)
∴ x = \(\frac{3 + \sqrt{13}}{2}\)
or x = \(\frac{3- \sqrt{13}}{2}\)
(ii) 1/x+4 – 1/x-7 = 11/30
⇒ x-7-x-4/(x+4)(x-7) = 11/30
⇒ -11/(x+4)(x-7) = 11/30
⇒ (x+4)(x-7) = -30
⇒ x2 – 3x – 28 = 30
⇒ x2 – 3x + 2 = 0
We can solve this equation by factorization method now,
⇒ x2 – 2x – x + 2 = 0
⇒ x(x – 2) – 1(x – 2) = 0
⇒ (x – 2)(x – 1) = 0
⇒ x = 1 or 2