Advertisements
Advertisements
Question
`x^2-4x+1=0`
Advertisements
Solution
`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
RELATED QUESTIONS
Solve the following quadratic equation for x : 4x2 − 4a2x + (a4 − b4) =0.
Solve the following quadratic equations by factorization:
4x2 + 5x = 0
Solve the following quadratic equations by factorization:
`2/2^2-5/x+2=0`
Solve the following quadratic equations by factorization:
ax2 + (4a2 − 3b)x − 12ab = 0
Solve the following quadratic equations by factorization:
`1/(x+4)-1/(x-7)=11/30` , x ≠ 4, 7
Two pipes running together can fill a tank in `11 1/9` minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.
Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0.
The value of c for which the equation ax2 + 2bx + c = 0 has equal roots is
Solve the following equation: `7"x" + 3/"x" = 35 3/5`
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
Solve the following quadratic equation using factorization method:
`"x"^2-11"x"+24=0`
The sum of the squares of three consecutive natural numbers is 110. Determine the numbers.
The speed of an express train is x km/hr arid the speed of an ordinary train is 12 km/hr less than that of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of 240 km, find the speed of the express train.
An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey the speed was increased by 40 km/hr. Write down the expression for the time taken for
the return Journey. If the return journey took 30 minutes less than the onward journey write down an equation in x and find its value.
Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
In each of the following determine whether the given values are solutions of the equation or not.
9x2 - 3x - 2 = 0; x = `-(1)/(3), x = (2)/(3)`
Solve the following equation by factorization
3(y2 – 6) = y(y + 7) – 3
Solve the following equation by factorization
5x2 – 8x – 4 = 0 when x∈Q
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
Solve the following equation by factorisation :
`sqrt(x + 15) = x + 3`
