Advertisements
Advertisements
Question
Solve the equation 2x `-(1)/x` = 7. Write your answer correct to two decimal places.
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
APPEARS IN
RELATED QUESTIONS
Find x in terms of a, b and c: `a/(x-a)+b/(x-b)=(2c)/(x-c)`
Find the consecutive even integers whose squares have the sum 340.
An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.
If the quadratic equation (c2 – ab) x2 – 2 (a2 – bc) x + b2 – ac = 0 in x, has equal roots, then show that either a = 0 or a3 + b3 + c3 = 3abc ?
If −5 is a root of the quadratic equation\[2 x^2 + px - 15 = 0\] and the quadratic equation \[p( x^2 + x) + k = 0\] has equal roots, find the value of k.
If the equation x2 − ax + 1 = 0 has two distinct roots, then
If the equation x2 − bx + 1 = 0 does not possess real roots, then
Solve equation using factorisation method:
`2x^2 - 1/2x = 0`
Solve the following quadratic equation by factorisation:
2x2 + ax - a2 = 0 where a ∈ R.
