Advertisements
Advertisements
प्रश्न
Solve the following equation by factorisation :
`sqrt(3x^2 - 2x - 1) = 2x - 2`
Advertisements
उत्तर
`sqrt(3x^2 - 2x - 1) = 2x - 2`
Squaring both sides
3x2 - 2x – 1 = (2x - 2)2
⇒ 3x2 – 2x – 1 = 4x2 – 8x + 4
⇒ 4x2 – 8x + 4 – 3x2 + 2x + 1 = 0
⇒ x2 – 6x + 5 = 0
⇒ x2 – 5x – x + 5 = 0
⇒ x(x – 5) –1(x – 5) = 0
⇒ (x – 5)(x – 1) = 0
Either x – 5 = 0,
then x = 5
or
x – 1 = 0,
then x = 1
Check :
(i) If x = 5, then
L.H.S. = `sqrt(3x^2 - 2x - 1)`
= `sqrt(3 xx (5)^2 - 2 xx 5 - 1)`
= `sqrt(3 xx 25 - 10 - 1)`
= `sqrt(75 - 10 - 1)`
= `sqrt(64)`
= 8
R.H.S. = 2x – 2
= 2 x 5 – 2
= 10 – 2
= 8
∵ L.H.S. = R.H.S.
∴ x = 5 is a root
(ii) If x = 1, then
L.H.S. = `sqrt(3x^2 - 2x - 1)`
= `sqrt(3(1)^2 - 2(1) - 1)`
= `sqrt(3 xx 1 - 2 - 1)`
= `sqrt(3 - 2 - 1)`
= 0
R.H.S. = 2x – 2
= 2 x 1 – 2
= 2 – 2
= 0
∵ L.H.S. = R.H.S.
∴ x = 1 is also its root
Hence x = 5, 1.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
3x2 = -11x - 10
Solve the following quadratic equations by factorization:
`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`, x ≠ 2, 4
The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.
Determine whether the values given against the quadratic equation are the roots of the equation.
x2 + 4x – 5 = 0 , x = 1, –1
If one root of the equation 4x2 − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =
Solve the following equation: `x^2 + (a + 1/a)x + 1 = 0`
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
Some students planned a picnic. The budget for the food was Rs. 480. As eight of them failed to join the party, the cost of the food for each member increased by Rs. 10. Find how many students went for the picnic.
Solve the following equation by factorization
x(2x + 5) = 3
Use the substitution y = 3x + 1 to solve for x : 5(3x + 1 )2 + 6(3x + 1) – 8 = 0
