Question

if x+1/x=-2, then x^96-x^95+x^86-​

Answer 1

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(x+1/x)²=3

x²+ 2 + 1/x²= 3

x² - 1 + 1/x²=0

x⁴– x² + 1 = 0. ,

Multiplying both sides by (x^2+1).

(x²+1).(x⁴-x²+1)= 0×(x²+1).

(x⁶ +1)= 0…………..(1)

Now

x²⁰⁶+x²⁰⁰+x⁹⁰+x⁸⁴+x¹⁸+x¹²+x⁶ + 1= ?

= x²⁰⁰.(x⁶+1)+x⁸⁴.(x⁶+1)+x¹².(x⁶+1)+1.(x⁶+1).

= (x⁶ +1).(x²⁰⁰+x⁸⁴+x¹²+1). , putting (x⁶ +1) =0 from eqn (1).

= 0 × (x²⁰⁰+x⁸⁴+ x¹² +1).

= 0. Answer.

Answer 2

72 = 72

96 = 96

first 69 and second 27 = 6927

58 × 87 = 58 × 85.

87 × 78

first 78 and second 85 = 7885

then. 79 × 86

•°• ANSWER = 6897

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