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
Solve for x
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 2, "where x" != -1/2, 1`
Solve the following quadratic equations by factorization:
x2 - x - a(a + 1) = 0
Solve the following quadratic equation by factorisation.
\[6x - \frac{2}{x} = 1\]
Show that x = −2 is a solution of 3x2 + 13x + 14 = 0.
The number of quadratic equations having real roots and which do not change by squaring their roots is
The value of c for which the equation ax2 + 2bx + c = 0 has equal roots is
If a and b are roots of the equation x2 + ax + b = 0, then a + b =
Solve the equation 2x `-(1)/x` = 7. Write your answer correct to two decimal places.
Solve the equation x4 + 2x3 - 13x2 + 2x + 1 = 0.
In each of the following, determine whether the given values are solution of the given equation or not:
x2 + x + 1 = 0; x = 0; x = 1
In each of the following, determine whether the given values are solution of the given equation or not:
`a^2x^2 - 3abx + 2b^2 = 0; x = a/b, x = b/a`.
Solve the following equation by factorization
4x2 = 3x
Solve the following equation by factorization
(x – 4)2 + 52 = 132
Solve the following equation by factorization
x2 – (p + q)x + pq = 0
There are three consecutive positive integers such that the sum of the square of the first and the product of other two is 154. What are the integers?
A two digit number contains the bigger at ten’s place. The product of the digits is 27 and the difference between two digits is 6. Find the number.
A rectangle of area 105 cm² has its length equal to x cm. Write down its breadth in terms of x. Given that the perimeter is 44 cm, write down an equation in x and solve it to determine the dimensions of the rectangle.
If 'p' is a root of the quadratic equation x2 – (p + q) x + k = 0, then the value of 'k' is ______.
For quadratic equation `2x + 5/x = 5` :
Which of the following is correct for the equation `1/(x - 3) - 1/(x + 5) = 1`?
