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
Solve the following quadratic equations by factorization:
`(x-3)/(x+3)-(x+3)/(x-3)=48/7` , x ≠ 3, x ≠ -3
Solve the following quadratic equations by factorization:
`1/(x-2)+2/(x-1)=6/x` , x ≠ 0
Solve the following quadratic equations by factorization:
`a/(x-a)+b/(x-b)=(2c)/(x-c)`
A passenger train takes 3 hours less for a journey of 360 km, if its speed is increased by 10 km/hr from its usual speed. What is the usual speed?
Solve the following quadratic equations by factorization:
`2(x^2 – 6) = 3 ( x – 4)`
Write the set of value of 'a' for which the equation x2 + ax − 1 = 0 has real roots.
If the equation x2 − ax + 1 = 0 has two distinct roots, then
A farmer wishes to grow a 100m2 rectangular vegetable garden. Since he was with him only 30m barbed wire, he fences 3 sides of the rectangular garden letting the compound of his house to act as the 4th side. Find the dimensions of his garden .
Solve the following equation by factorization
6p2+ 11p – 10 = 0
Solve the following equation by factorisation :
`sqrt(x + 15) = x + 3`
