Advertisements
Advertisements
प्रश्न
Solve for x: `1/(x+1)+2/(x+2)=4/(x+4), `x ≠ -1, -2, -3
Advertisements
उत्तर
`1/(x+1)+2/(x+2)=4/(x+4)`
L.C.M. of all the denominators is (x + 1)(x + 2)(x + 4)
Multiply throughout by the L.C.M.,we get
(x + 2)(x + 4) + 2(x + 1)(x + 4) = 4(x + 1)(x + 2)
∴ (x + 4)(x + 2 + 2x + 2) = 4(x2 + 3x + 2)
∴ (x + 4)(3x + 4) 4x2 + 12x + 8
∴ 3x2 + 16x + 16 = 4x2 + 12 x 8
∴ x2-4x-8=0
Now,a = 1,b = -4,c = -8
`x=(-b+-sqrt(b^2-4ac))/(2a)=(4+-sqrt(16+32))/2=(4+-sqrt48)/2=(4+-4sqrt3)/2`
`:.x=2+-2sqrt3`
APPEARS IN
संबंधित प्रश्न
Determine the nature of the roots of the following quadratic equation:
`3x^2-2sqrt6x+2=0`
Find the values of k for which the roots are real and equal in each of the following equation:
5x2 - 4x + 2 + k(4x2 - 2x - 1) = 0
For what value of k, (4 - k)x2 + (2k + 4)x + (8k + 1) = 0, is a perfect square.
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
x2 + 4x + 5 = 0
Find if x = – 1 is a root of the equation 2x² – 3x + 1 = 0.
If `(2)/(3)` and – 3 are the roots of the equation px2+ 7x + q = 0, find the values of p and q.
Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
The sum of all integral values of k(k ≠ 0) for which the equation `2/(x - 1), 1/(x - 2) = 2/k` in x has no real roots, is ______.
