Advertisements
Advertisements
प्रश्न
`x^2-4x+1=0`
Advertisements
उत्तर
`x^2-4x+1=0`
⇒`x^2-4x=1`
⇒`x^2-2xx x xx2+2^2=-1+2^2` (Adding `2^2`on both sides)
⇒`(x-2)^2=+-sqrt3`
⇒`x-2=+-sqrt3` (Taking square root on the both sides)
⇒`x-2=sqrt3 or x-2=-sqrt3`
⇒`x=2+sqrt3 or x=2-sqrt3`
Hence, `2+sqrt3 and 2-sqrt3` are the roots of the given equation.
APPEARS IN
संबंधित प्रश्न
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Two number differ by 4 and their product is 192. Find the numbers?
A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
Solve:
`(x/(x + 2))^2 - 7(x/(x + 2)) + 12 = 0; x != -2`
Solve the following quadratic equation for x:
`4sqrt3x^3+5x-2sqrt3=0`
The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train.
Find the roots of the quadratic equation \[\sqrt{2} x^2 + 7x + 5\sqrt{2} = 0\].
Show that x = −3 is a solution of x2 + 6x + 9 = 0.
If the roots of the equations \[\left( a^2 + b^2 \right) x^2 - 2b\left( a + c \right)x + \left( b^2 + c^2 \right) = 0\] are equal, then
If one root the equation 2x2 + kx + 4 = 0 is 2, then the other root is
Find two natural numbers which differ by 3 and whose squares have the sum of 117.
Solve equation using factorisation method:
`5/("x" -2) - 3/("x" + 6) = 4/"x"`
A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and Solve it to find the original cost of the books.
Solve the following quadratic equation by factorisation:
x2 + 3x - 18 = 0
In each of the following, determine whether the given values are solution of the given equation or not:
`x = 1/x = (13)/(6), x = (5)/(6), x = (4)/(3)`
Solve the following equation by factorization
3(x – 2)2 = 147
Find the values of x if p + 7 = 0, q – 12 = 0 and x2 + px + q = 0,
If x = p is a solution of the equation x(2x + 5) = 3, then find the value of p.
Solve the quadratic equation by factorisation method:
x2 – 15x + 54 = 0
