Advertisements
Advertisements
प्रश्न
Solve the following equation by factorization:
`x^2 - (1 + sqrt(2))x + sqrt(2) = 0`
Advertisements
उत्तर १
`x^2 - (1 + sqrt(2))x + sqrt(2) = 0`
⇒ `x^2 - x - sqrt(2)x + sqrt(2) = 0`
⇒ `(x - 1) - sqrt(2) (x - 1)= 0`
⇒ `(x - 1) (x - sqrt(2)) = 0`
Either x – 1 = 0,
Then x = 1
or
`x - sqrt(2) = 0`,
Then x = `sqrt(2)`
Hence x = 1, `sqrt(2)`.
उत्तर २
Given,
⇒ `x^2 - (1 + sqrt(2))x + sqrt(2) = 0`
⇒ `x^2 - 1x - sqrt(2)x + sqrt(2) = 0`
⇒ `x(x - 1) - sqrt(2)(x - 1) = 0`
⇒ `(x - sqrt(2))(x - 1) = 0`
⇒ `(x - sqrt(2)) = 0` or (x – 1) = 0 ...[Using zero-product rule]
⇒ `x = sqrt(2)` or x = 1
Hence, `x = {1, sqrt(2)}`.
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`1/((x-1)(x-2))+1/((x-2)(x-3))+1/((x-3)(x-4))=1/6`
The sum of two numbers is 48 and their product is 432. Find the numbers?
Find the two consecutive positive odd integers whose product is 483.
The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.
Solve the following quadratic equation by factorisation.
x2 – 15x + 54 = 0
Solve the following quadratic equations by factorization:
\[\sqrt{3}x^2 - 2\sqrt{2}x - 2\sqrt{3} = 0\]
The positive value of k for which the equation x2 + kx + 64 = 0 and x2 – 8x + k = 0 will both have real roots, is ______.
A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.
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
3x2 – 5x – 12 = 0
