Question

if 1 / (x-5) = A / x-5 + 1 / 2(x-7) then find the A​

Answer 1

Answer:

x+1/x=6 ……………..(1)

Squaring both sides

x^2+1/x^2+2=36

x^2+1/x^2=34 ………..(2)

On cubing eq.(1) both sides

x^3+1/x^3+3.x1/x.(x+1/x)=216

x^3+1/x^3+3×6=216

x^3+1/x^3=216–18

x^3+1/x^3=198………………(3)

Multiply eq.(2) & (3)

(x^2+1/x^2)×(x^3+1/x^3)=34×198

x^5+x+1/x+1/x^5=6732

x^5+6+1/x^5=6732

x^5+1/x^5=6732–6=6726 , Answer