Advertisements
Advertisements
प्रश्न
Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 0`.
उत्तर
Given equation `9^(x + 2) -6.3^(x + 1) + 1 = 0`
⇒ 9x.92 - 6.3x.31 + 1 = 0
⇒ 81.(32)x - 18.3x + 1 = 0
⇒ 81.32x - 18.3x + 1 = 0
Putting 3x = y, then it becomes 81y2 - 18y + 1 = 0
⇒ 81y2 - 9y - 9y + 1 = 0
⇒ 9y(9y - 1) -1(9y - 1) = 0
⇒ (9y - 1) (9y - 1) = 0
⇒ 9y = 1
⇒ y = `(1)/(9)`
But 3x = `(1)/(9) = (1)/(3^2) = 3^-2`
∴ x = -2
Hence, the required root is -2.
APPEARS IN
संबंधित प्रश्न
Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.
Find the values of k for which the roots are real and equal in each of the following equation:
2kx2 - 40x + 25 = 0
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 6x + 1 = 0
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
Find the value of the discriminant in the following quadratic equation :
10 x - `1/x` = 3
Solve the following quadratic equation using formula method only
15x2 - 28 = x
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" - 1 = 0`
Which of the following equations has 2 as a root?
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
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 ______.
