Question

if x/b+b/x=a/b+b/a find the roots of the equation​

Answer 1

Answer:

(X+b)/(a-b)=(x-b)/(a+b) (x+b)(a+b)=(a-b)(x-b) ax+bx+ab+b² = ax-ab-bx+b² bx+ab = -ab-bx 2bx= -2ab x= -a.

(X+b)/(a-b)=(x-b)/(a+b) (x+b)(a+b)=(a-b)(x-b) ax+bx+ab+b² = ax-ab-bx+b² bx+ab = -ab-bx ...

(x+b)/(a-b) = (x-b)/(a+b). or (x+b)/(x-b) = (a-b)/(a+b) . Apply componendo and dividendo ...

Answer 2

Answer:

x = a and x = b²/a

Step-by-step explanation:

x/b + b/x = a/b + b/a

=> (x²+b²)/bx = (a²+b²)/ab

=> (x²+b²)ab = (a²+b²)bx

[b can be cancelled out]

=> ax² + ab² = a²x + b²x

=> ax² - (a²+b²)x + ab² = 0

where, a = a , b = -(a²+b²) , c = ab²

=> ax² -a²x - b²x + ab² = 0

=> ax(x - a) - b²(x-a) = 0

=> (x-a)(ax-b²) = 0

=> x= a , x = b²/a

verification,

sum of roots = -b/a

=> a + b²/a = -{-(a²+b²)}\a

=> (a²+b²)/a = (a²+b²)/a

product of roots = c/a

=> a × b²/a = ab²/a

=> b² = b²

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