Advertisements
Advertisements
Question
Solve for x:
4x2 + 4bx − (a2 − b2) = 0
Advertisements
Solution
The given quadratic equation is.`4x^2+4bx-(a^2-b^2)=0`
`4x^2+2(a+b)x-2(a-b)x-(a^2-b^2)=0`
`2x(2x+a+b)-(a-b)(2x+a+b)=0`
Therefore,
`2x-(a-b)=0`
`2x=a-b`
`x=(a-b)/2`
or
`2x+a+b=0`
`2x=a-b`
`x=(a-b)/2`
or
`2x+a+b=0`
`2x=-(a+b)`
`x=-(a-b)/2`
Thus, the solutions of the given quadratic equation are
APPEARS IN
RELATED QUESTIONS
Divide 29 into two parts so that the sum of the squares of the parts is 425.
Solve the following quadratic equations by factorization:
`2(x^2 – 6) = 3 ( x – 4)`
Solve the following quadratic equations by factorization:
`(x + 3)^2 – 4(x + 3) – 5 = 0 `
Solve the following quadratic equations by factorization:
\[16x - \frac{10}{x} = 27\]
Solve the following equation: 25x (x + 1) = -4
Solve the following equation: a2b2x2 + b2x - a2x - 1 = 0
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + `sqrt(2)` - 4 = 0; x = `sqrt(2)`, x = -2`sqrt(2)`
Solve the following equation by factorization
`(1)/(7)(3x – 5)^2`= 28
If x = 3 is one root of the quadratic equation 2x2 + px + 30 = 0, find the value of p and the other root of the quadratic equation.
