Advertisements
Advertisements
प्रश्न
Solve for x: `1/(x+1)+2/(x+2)=4/(x+4), `x ≠ -1, -2, -3
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
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 4kx + k = 0
If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
`10x -(1)/x` = 3
`(2)/x^2 - (5)/x + 2` = 0
Choose the correct answer from the given four options :
If the equation 2x² – 6x + p = 0 has real and different roots, then the values of p are given by
Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x2 + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
If the root of the given quadratic equation are real and equal, then find the value of ‘k’ X2 + 2X + k = 0
α and β are the roots of 4x2 + 3x + 7 = 0, then the value of `1/α + 1/β` is:
If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
