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 the following quadratic equations by factorization:
`x^2-4sqrt2x+6=0`
Solve the following quadratic equations by factorization:
`1/(x+4)-1/(x-7)=11/30` , x ≠ 4, 7
The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m2, what are the length and breadth of the hall?
Solve the given quadratic equation for x : 9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0 ?
Solve the following quadratic equation by
factorisation.
5m2 = 22m + 15
Solve the following quadratic equation by factorization: \[\frac{a}{x - b} + \frac{b}{x - a} = 2\]
If the sum of the roots of the equation \[x^2 - \left( k + 6 \right)x + 2\left( 2k - 1 \right) = 0\] is equal to half of their product, then k =
Solve the following equation: `"a"("x"^2 + 1) - x("a"^2 + 1) = 0`
The product of a girl's age five years ago and her age 3 years later is 105. Find her present age.
Solve the following equation by factorization
x(6x – 1) = 35
