Advertisements
Advertisements
प्रश्न
Solve the following equation by factorization
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
Advertisements
उत्तर
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
⇒ `(1)/(2a + b + 2x) = (1)/(2x) + (1)/(2a) + (1)/(b)`
⇒ `(2x - (2a + b + 2x))/((2a + b + 2x)2x) = (b + 2a)/(2ab)`
⇒ `(-(2a + b))/((2a + b + 2x)2x) = ((2a + b))/(2ab)`
⇒ `(-1)/((2a + b + 2x)2x) = (1)/(2ab)`
⇒ -2ab = (2a + b + 2x)2x
⇒ 4ax + 2xb + 4x2 = -2ab
⇒ 4x2 + 2bx + 4ax + 2ab = 0
⇒ 2x(2x + b) + 2a(2x + b) = 0
⇒ (2x + 2a)(2x + b) = 0
⇒ 2x + 2a = 0 or 2x + b = 0
`x = -a or x = -b/(2)`
Hence, the roots of the given equation are
`-a and -b/(2)`.
APPEARS IN
संबंधित प्रश्न
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects
Solve the following quadratic equations by factorization:
5x2 - 3x - 2 = 0
Solve the following quadratic equations by factorization:
`1/x-1/(x-2)=3` , x ≠ 0, 2
The sum of a number and its reciprocal is 17/4. Find the number.
The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
`2x^2+5x-3=0`
Solve the following equation by factorization
3x2= x + 4
Solve the following equation by factorization
a2x2 + (a2+ b2)x + b2 = 0, a ≠ 0
A person was given Rs. 3000 for a tour. If he extends his tour programme by 5 days, he must cut down his daily expenses by Rs. 20. Find the number of days of his tour programme.
The speed of a boat in still water is 11 km/ hr. It can go 12 km up-stream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream
