Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
(a + b)2x2 - 4abx - (a - b)2 = 0
उत्तर
We have been given
(a + b)2x2 - 4abx - (a - b)2 = 0
(a + b)2x2 - (a + b)2x + (a - b)2x - (a - b)2 = 0
(a + b)2x(x - 1) + (a - b)2(x - 1) = 0
((a + b)2x + (a - b)2)(x - 1) = 0
Therefore,
(a + b)2x + (a - b)2 = 0
(a + b)2x = - (a - b)2
`x=-((a-b)/(a+b))^2`
or,
x - 1 = 0
x = 1
Hence, `x=-((a-b)/(a+b))^2` or x = 1
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations
(i) x2 + 5x = 0 (ii) x2 = 3x (iii) x2 = 4
Solve the following quadratic equation by factorisation.
3x2 - 2√6x + 2 = 0
Solve the following quadratic equations by factorization:\[\frac{1}{x - 3} + \frac{2}{x - 2} = \frac{8}{x}; x \neq 0, 2, 3\]
Solve the following quadratic equations by factorization: \[\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 4 - \frac{2x + 3}{x - 2}; x \neq 1, - 2, 2\]
Write the number of real roots of the equation x2 + 3 |x| + 2 = 0.
If one of the equation x2 + ax + 3 = 0 is 1, then its other root is
Solve equation using factorisation method:
x2 – (a + b)x + ab = 0
The length of verandah is 3m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.
(i) Taking x, breadth of the verandah write an equation in ‘x’ that represents the above statement.
(ii) Solve the equation obtained in above and hence find the dimension of verandah.
Paul is x years old and his father’s age is twice the square of Paul’s age. Ten years hence, the father’s age will be four times Paul’s age. Find their present ages.
Solve the following equation by factorisation :
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
