Advertisements
Advertisements
प्रश्न
Solve the following equation by factorization
`sqrt(3x + 4) = x`
Advertisements
उत्तर
`sqrt(3x + 4) = x`
Squaring on both sides
3x + 4 = x2
⇒ x2 - 3x - 4 = 0
⇒ 4x + x - 4 = 0
⇒ x(x - 4) + 1(x - 4) = 0
⇒ (x - 4)(x + 1) = 0
Either x - 4 = 0,
then x = 4
or
x + 1 = 0,
then x = -1
∴ x = 4, - 1
Check
(i) If x = 4, then
L.H.S.
= `sqrt(3x + 4)`
= `sqrt(3 xx 4 + 4)`
= `sqrt(12 + 4)`
= `sqrt(16)`
= 4
R.H.S.
= x
= 4
∴ L.H.S. = R.H.S.
Hence x = 4 is its root
(ii) If x = -1, then
L.H.S.
= `sqrt(3x(-1) + 4)`
= `sqrt(-3 + 4)`
= `sqrt(1)`
= 1
R.H.S.
= x
= -1
∵ L.H.S. ≠ R.H.S.
∴ x = -1 is not its root,
Hence x = 4.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
x2 + 2ab = (2a + b)x
Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.
Solve each of the following equations by factorization:
`X^2 – 10x – 24 = 0 `
The difference of two natural number is 3 and the difference of their reciprocals is `3/28`Find the numbers.
A teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
Solve the following quadratic equation using formula method only
x2 - 7x - 5 = 0
Solve the following equation by factorization
6p2+ 11p – 10 = 0
A boat can cover 10 km up the stream and 5 km down the stream in 6 hours. If the speed of the stream is 1.5 km/hr. find the speed of the boat in still water.
Paul is x years old and his father’s age is twice the square of Paul’s age. Ten years hence, the father’s age will be four times Paul’s age. Find their present ages.
If 'p' is a root of the quadratic equation x2 – (p + q) x + k = 0, then the value of 'k' is ______.
