Question

If x+1/x=4,then find x⁴+1/x⁴.


with process(in book if possible please).​

Answer 1

Answer:

Squaring both sides,

(x + 1/x)² = 4²

x² + 1/x² + 2×x×1/x = 16

x² + 1/x² + 2 = 16

x² + 1/x² = 14

Now, again squaring both sides,

(x² + 1/x²)² = 14²

x⁴ + 1/x⁴ + 2×x²×1/x²  = 196

x⁴ + 1/x⁴ + 2 = 196

∴ x⁴ + 1/x⁴ = 194

Answer 2

Answer

194

Step-by-step explanation:

194x+1/x=4

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

=x^2+2(x)(1/x)+(1/x)^2=16

=x^2+2+1/x^2=16

=x^2+1/x^2=16-2

=x^2+1/x^2=14

Now,

(x^2+1/x^2)^2=14^2

x^4+2(x^2)(1/x^2)+1/x^4=196

x^4+2+1/x^4= 196

x^4+1/x^4=196-2

x^4+1/x^4=194