Advertisements
Advertisements
Question
Solve the following quadratic equation:
4x2 - 4ax + (a2 - b2) = 0 where a , b ∈ R.
Advertisements
Solution
4x2 - 4ax + (a2 - b2) = 0 where a , b ∈ R
⇒ 4x2 - {2(a + b)x + 2(a - b)x} + a2 - b2 = 0
⇒ {4x2 - 2(a + b)x} - {2(a - b)x - (a2 - b2)} = 0
⇒ 2x{2x - (a + b)} - (a - b) {2x - (a + b)} = 0
⇒ {2x - (a + b)} {2x - (a - b)} = 0
⇒ 2x - (a + b) = 0
or
2x - (a - b) = 0
⇒ x = `(a + b)/(2)` or x = `(a - b)/(2)`.
RELATED QUESTIONS
The sum of a number and its reciprocal is 17/4. Find the number.
The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he returned at a speed of 10 km/hr more than the speed of going, what was the speed per hour in each direction?
Solve:
x(x + 1) + (x + 2)(x + 3) = 42
Solve the following quadratic equations by factorization:
`5/(x - 2) - 3/(x + 6) = 4/x`
Solve the following equation: `("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
In each of the following determine whether the given values are solutions of the equation or not.
9x2 - 3x - 2 = 0; x = `-(1)/(3), x = (2)/(3)`
Solve the following equation by factorization
(x – 3) (2x + 5) = 0
Solve the following equation by factorization
(x – 4)2 + 52 = 132
Divide 16 into two parts such that the twice the square of the larger part exceeds the square of the smaller part by 164.
If `x + 1/x = 2.5`, the value of x is ______.
