Math, asked by nidumolphani, 5 months ago

if x+1/x=4, then find the value of x²[x²+1/x^6]+[x³+1/x³]


⇄pls answer i will mark as brainalist⇄

Answers

Answered by bson
0

Step-by-step explanation:

x + 1/x =4

squar on both sides gives

x² + 1/x² +2 =16

x²+1/x² =14

square on both sides

x⁴+1/x⁴+2 = 196

x⁴+1/x⁴=194

x+ 1/x =4

cube on both sides

x³ +1/x³ +3*x*1/x*(x+1/x) = 64

x³+1/x³ +3×1×4 =64

x³+1/x³ +12 =64

x³+1/x³=52

given x²(x²+ 1/x⁶) +(x³+1/x³)

= x⁴ +1/x⁴ + x³+1/x³

= 194+52

= 246

Answered by wingschicken74961
0

Answer:

=x^2[x^2+1/x^6]+[x^3+1/x^3]

=[(x^2+1)/x^4]+[(x^3+1)/x^3]

=[(x^2+1)+x(x^3+1)]/x^4

=(x^2+1+x^4+x)/x^4

=(x^4+x^2+x+1)/x^4

=1+1/x^2+1/x^3+1/x^4

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