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