Advertisements
Advertisements
प्रश्न
Solve the following quadratic equation for x:
x2 − 4ax − b2 + 4a2 = 0
उत्तर
The given quadratic equation is x2 − 4ax − b2 + 4a2 = 0
∴ x2 + (−4a)x − (4a2 + b2)= 0 [A = 1, B = −4a, C = 4a2 − b2]
`rArr x=(-(-4a)+-sqrt((-4a)^2-4xxlxx(4a^2-b^2)))/2` `[therefore x= (-B+-sqrtB^2-4AC)/(2A)]`
`rArr x=(4a+-sqrt(16^2-16a^2+4b^2))/2`
`rArr x=(4a+-sqrt4b^2)/2`
`rArr x=(4a+-2b)/2`
`rArr x=2a+-b`
`therefore x=2a+-b` `or` `x=2a-b`
Thus, the solution of the given quadratic equation is x = 2a + b or x = 2a − b.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`10x-1/x=3`
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.
Some students planned a picnic. The budget for food was Rs. 480. But eight of these failed to go and thus the cost of food for each member increased by Rs. 10. How many students attended the picnic?
Solve the following quadratic equation by factorisation.
\[25 m^2 = 9\]
Solve the following quadratic equations by factorization: \[\frac{2}{x + 1} + \frac{3}{2(x - 2)} = \frac{23}{5x}; x \neq 0, - 1, 2\]
A two digit number is such that the product of its digit is 14. When 45 is added to the number, then the digit interchange their places. Find the number.
Solve the following equation by factorization
`(2)/(x^2) - (5)/x + 2 = 0, x ≠ 0`
A shopkeeper buys a certain number of books for Rs 960. If the cost per book was Rs 8 less, the number of books that could be bought for Rs 960 would be 4 more. Taking the original cost of each book to be Rs x, write an equation in x and solve it to find the original cost of each book.
Ritu bought a saree for Rs. 60x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.
The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find the present age.
