Advertisements
Advertisements
प्रश्न
Solve the following equation by factorisation :
`sqrt(x + 15) = x + 3`
Advertisements
उत्तर
`sqrt(x + 15) = x + 3`
Squaring on both sides
x + 15 = (x + 3)2
⇒ x2 + 6x + 9 – x – 15 = 0
⇒ x2 + 5x – 6 = 0
⇒ x2 + 6x – x – 6 = 0
⇒ x(x + 6) –1(x + 6) = 0
⇒ (x + 6)(x – 1) = 0
Either x + 6 = 0,
then x = -6
or
x – 1 = 0,
then x = 1
∴ x = –6, 1
Check :
(i) If x = –6 then
L.H.S. = `sqrt(x + 15)`
= `sqrt(-6 + 15)`
= `sqrt(9)`
= 3
R.H.S. = x + 3
= –6 + 3
= –3
∵ L.H.S. ≠ R.H.S.
∴ x = –6 is not a root
(ii) If x = 1, then
L.H.S. - `sqrt(x + 15)`
= `sqrt(1 + 15)`
= `sqrt(16)`
= 4
R.H.S. = x + 3
= 1 + 3
= 4
∵ L.H.S. = R.H.S.
∴ x = 1 is a root of this equation
Hence x = 1.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`(x-1/2)^2=4`
Solve the following quadratic equations by factorization:
`m/nx^2+n/m=1-2x`
Solve the following quadratic equations by factorization:
`x^2 – (a + b) x + ab = 0`
`x^2+8x-2=0`
Solve the following quadratic equation by factorisation.
\[6x - \frac{2}{x} = 1\]
Solve the following equation: abx2 +(b2-ac) x - bc = 0
Solve the following quadratic equation using formula method only
x2 - 7x - 5 = 0
Solve equation using factorisation method:
`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`
A two digit number is such that the product of the digits is 12. When 36 is added to this number the digits interchange their places. Determine the number.
Solve the quadratic equation: x2 – 2ax + (a2 – b2) = 0 for x.
