Question

(a-x)^5+(x-b)^5=(a-b)^5 find value of x​

Answer 1

Answer:

x={ (a+b) ± √(a-b) ( a--b-4) } / 2

Step-by-step explanation:

(a-x)^5+(x-b)^5=(a-b)^5

taking log

5 log(a-x)+5 log(x-b)=5 log(a-b)

log(a-x)+log(x-b) = log(a-b)

log(a-x)(x-b)=(a-b)

(a-x)(x-b)=a-b

ax-ab-x²+bx=a-b

x²-(a+b)x+a-b+ab=0

x= { (a+b) ±√(a+b)²-4(a-b+ab) }/2

={ (a+b) ±√(a²+b²+2ab-4a+4b-4ab)}/2

={ (a+b) ±√(a²+b²-2ab-4a+4b)}/2

={ (a+b) ±√(a-b)²-4(a-b)}/2

x={ (a+b) ± √(a-b) ( a--b-4) } / 2