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:
(a + b)2x2 - 4abx - (a - b)2 = 0
Solve each of the following equations by factorization:
`X^2 – 10x – 24 = 0 `
Solve the following quadratic equations by factorization:
`(3x-2)/(2x-3)=(3x-8)/(x+4)`
Find the value of k for which the following equations have real and equal roots:
\[\left( k + 1 \right) x^2 - 2\left( k - 1 \right)x + 1 = 0\]
Is there any real value of 'a' for which the equation x2 + 2x + (a2 + 1) = 0 has real roots?
Solve the following equation by factorization
4x2 = 3x
Rs. 7500 is divided equally among a certain number of children. Had there been 20 less children, each would have receive Rs 100 more. Find the original number of children.
The hotel bill for a number of people for an overnight stay is Rs. 4800. If there were 4 more, the bill each person had to pay would have reduced by Rs. 200. Find the number of people staying overnight.
For quadratic equation `2x + 5/x = 5` :
The product of two integers is –18; the integers are ______.
