Advertisements
Advertisements
Question
Solve the following equation by factorization
`sqrt(3x + 4) = x`
Solution
`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
RELATED QUESTIONS
Solve (i) x2 + 3x – 18 = 0
(ii) (x – 4) (5x + 2) = 0
(iii) 2x2 + ax – a2 = 0; where ‘a’ is a real number
`2x^2+5x-3=0`
If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax2 +bx + 1 = 0 having real roots is
Solve the following equation: `("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
Two pipes flowing together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.
In each of the following, determine whether the given values are solution of the given equation or not:
2x2 - x + 9 = x2 + 4x + 3; x = 2, x = 3
Solve the following equation by factorization
21x2 – 8x – 4 = 0
Solve the following equation by factorization.
a2x2 + 2ax + 1 = 0, a ≠ 0
Mohini wishes to fit three rods together in the shape of a right triangle. If the hypotenuse is 2 cm longer than the base and 4 cm longer than the shortest side, find the lengths of the rods.
The length of a rectangular garden is 12 m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden.
