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Question
Solve the equation 2x `-(1)/x` = 7. Write your answer correct to two decimal places.
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Solution
Solve the equation 2x `-(1)/x` = 7
2x2 - 1 = 7x
2x2 - 7x - 1 = 0
For quadratic equation ax2 + bx + c = 0
x = `(-b ± sqrt(2^2 - 4ac))/(2a)`
Here, a = 2, b = -7, c = -1
Therefore,
x = `(-(-7) ± sqrt((-7)^2 - 4 xx 2 xx (-1)))/(2 xx 2)`
x = `(7 ± sqrt(49 + 8))/(4)`
= `(7 ± sqrt(57))/(4)`
= `(7 + sqrt(57))/(4)` or x = `(7 - sqrt(57))/(4)`
x = `(7 + 7·550)/(4)` or x = `(7 - 7·550)/(4)`
x = 3·64 or x = -·14
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