Advertisements
Advertisements
Question
Solve the following equation: `("a+b")^2 "x"^2 - 4 "abx" - ("a - b")^2 = 0`
Advertisements
Solution
`("a+b")^2 "x"^2 - 4 "abx" - ("a - b")^2 = 0`
As, - (a + b)2 + (a - b)2 = - a2 - b2 - 2ab + a2 + b2 - 2ab = - 4ab
(a+b)2x2 -[(a+ b)2-(a-b)2] x - (a - b)2 = 0
(a+ b)2x2 - (a+ b)2x + (a - b)2x - (a - b)2 = 0
{(a+ b)2x} (x - 1) + {(a - b)2} (x - 1) = 0
(x - 1) [(a + b)2x + (a - b)2] = 0
x - 1 = 0 and (a + b)2x + (a - b)2 = 0
x = 1 and x = `-("a" - "b")^2/("a" + "b")^2`
x = 1 and x = `-(("a" - "b")/("a" + "b"))^2`
APPEARS IN
RELATED QUESTIONS
Solve for x :
`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
Solve the following quadratic equations by factorization:
(x − 4) (x + 2) = 0
The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.
The product of Ramu’s age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu’s present age.
Determine whether the values given against the quadratic equation are the roots of the equation.
x2 + 4x – 5 = 0 , x = 1, –1
Find the value of k for which the following equations have real and equal roots:
\[x^2 + k\left(2x + k - 1 \right) + 2 = 0\]
If \[x = - \frac{1}{2}\],is a solution of the quadratic equation \[3 x^2 + 2kx - 3 = 0\] ,find the value of k.
Solve equation using factorisation method:
`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`
If `x + 1/x = 2.5`, the value of x is ______.
