Advertisements
Advertisements
प्रश्न
Solve `9("x"^2 + 1/"x"^2) -3("x" - 1/"x") - 20 = 0`
उत्तर
`9[("x" - 1/"x")^2 + 2] -3 ("x" - 1/"x") - 20 = 0`
Let x - `1/"x" = "m"`
`9("m"^2 + 2) -3"m" -20 = 0`
`9"m"^2 + 18 - 3"m" - 20 = 0`
`9"m"^2 - 3"m" - 2 = 0`
9m2 - 6m + 3m - 2 = 0
3m (3m - 2) + 1(3m - 2) = 0
(3m - 2) (3m + 1) = 0
3m - 2 = 0 Or 3m + 1 = 0
3m = 2 Or 3m = -1
m = `2/3` Or m = `(-1)/3`
Resubstituting m = x - `1/x`
|
m = `2/3` x - `1/x = 2/3` Or `(x^2 - 1)/x = 2/3` 3x2 - 3 = 2x 3x2 - 2x - 3 = 0 Comparing with ax2 + bx + c = 0 a = 3, b = -2, c = -3 b2 - 4ac = (-2)2 - 4 (3) (-3) = 4 + 36 = 40 By formula method x = `-b ± sqrt(b^2 - 4ac)/"2a"` = `(2 ± sqrt40)/"2(3)"` = `(2 ± 2sqrt10)/6` = `(2 (1 ± sqrt10))/6` x = `(1 ± sqrt10)/3` |
m = `(-1)/3` x - `1/x = (-1)/3` `("x"^2 - 1)/"x" = (-1)/3` 3x2 - 3 = -x Comparing with ax2 + bx + c = 0 a = 3, b = 1, c = -3 b2 - 4ac = 12 - 4 (3) (-3) = 1+ 36 = 37 By formula method x = `-b ± sqrt(b^2 - 4ac)/"2a"` = `(-1 ± sqrt37)/"2(3)"` x = `(-1 ± sqrt37)/6` |
APPEARS IN
संबंधित प्रश्न
Check whether the following is the quadratic equation:
x2 - 2x = (-2)(3 - x)
Find the value of discriminant (Δ) for the quadratic equation: `x^2+7x+6=0`
Solve the quadratic equation x2 – 3(x + 3) = 0; Give your answer correct to two significant figures.
In the following, determine whether the given values are solutions of the given equation or not:
2x2 - x + 9 = x2 + 4x + 3, x = 2, x =3
Find the value of ‘m’, if the following equation has equal roots:
(m – 2)x2 – (5 + m)x + 16 = 0
Solve `9/2 x = 5 + x^2`
Solve `6/x = 1 + x`
Solve : x² – (a + b)x + ab = 0
Solve the following equation for x and give, in the following case, your answer correct to 2 decimal places:
2x2 – 10x + 5 = 0
Solve the following equation for x and give, in the following case, your answer correct to 2 decimal places:
`4x + 6/x + 13 = 0`
Solve: (2x+3)2 = 81
Determine whether x = − 1 is a root of the equation `x^2 − 3x + 2 = 0 `or not.
Solve the following equation using the formula:
`x^2 - 6 = 2sqrt(2)x`
Without solving, comment upon the nature of roots of the following equation:
25x2 − 10x + 1 = 0
Which of the following are quadratic equation in x?
`x^2-1/x^2=5`
Solve :
`3x^2 - 2sqrt6x + 2 = 0`
Examine whether the equation 5x² -6x + 7 = 2x² – 4x + 5 can be put in the form of a quadratic equation.
Solve the following equation by using formula :
`2x^2 + sqrt(5) - 5` = 0
If the sum of the roots of a quadratic equation is 5 and the product of the roots is also 5, then the equation is:
If x2 – 2x – 3 = 0; values of x correct to two significant figures are ______.
