Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
`x^2+(a+1/a)x+1=0`
Advertisements
उत्तर
We have been given
`x^2+(a+1/a)x+1=0`
`x^2+ax+1/ax+1=0`
`x(x+a)+1/a(x+a)=0`
`(x+1/a)(x+a)=0`
Therefore,
`x+1/a=0`
`x=-1/a`
or,
x + a = 0
x = -a
Hence, `x=-1/a` or x = -a
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation by Factorisation method: x2 + 7x + 10 = 0
Solve for x
:`1/((x-1)(x-2))+1/((x-2)(x-3))=2/3` , x ≠ 1,2,3
Solve the equation `4/x-3=5/(2x+3); xne0,-3/2` for x .
Find the roots of the following quadratic equation by factorisation:
x2 – 3x – 10 = 0
Solve the following quadratic equations by factorization:
25x(x + 1) = -4
Solve the following quadratic equations by factorization:
`x^2-4sqrt2x+6=0`
Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.
Find the consecutive even integers whose squares have the sum 340.
The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.
One of the roots of equation 5m2 + 2m + k = 0 is `(-7)/5` Complete the following activity to find the value of 'k'.
Solve the following quadratic equation by factorisation.
\[6x - \frac{2}{x} = 1\]
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.
Three years ago, a man was 5 times the age of his son. Four years hence, he will be thrice his son's age. Find the present ages of the man and his son.
In each of the following determine whether the given values are solutions of the equation or not
2x2 - 6x + 3 = 0; x = `(1)/(2)`
In each of the following determine whether the given values are solutions of the equation or not.
x2 + x + 1 = 0; x = 1, x = -1.
Solve the following equation by factorization
3(x – 2)2 = 147
Solve the following equation by factorization
a2x2 + (a2+ b2)x + b2 = 0, a ≠ 0
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by `(1)/(14)`. Find the fraction.
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.
If the sum of the roots of the quadratic equation ky2 – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.
