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Question
Solve the following equation by using quadratic formula and give your answer correct to 2 decimal places : `2x - (1)/x = 1`
Solution
`2x - (1)/x = 1`
⇒ 2x2 - 1 = 7x
⇒ 2x2 - 7x - 1 = 0 ....(i)
Comparing (i) with ax2 + bx + c, we get,
a = 2, b = -7, c = -1
∵ x = `(-b ± sqrt(b^2 - 4ac))/(2a)`
⇒ x = `(-(-7) ± sqrt((-7)^2 - 4(2) xx (-1)))/(2 xx 2)`
⇒ `(7 ± sqrt(49 + 8))/(4)`
⇒ `(7 ± sqrt(57))/(4)`
⇒ `x = (7 + sqrt(57))/(4) or x = (7 - sqrt(57))/(4)`
⇒ `x = (7 + 7.55)/(4) or x = (7 - 7.55)/(4)`
⇒ `x = (14.55)/(4) or x = (-0.55)/(4)`
⇒ x = 3.64 or x = -0.14.
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