Question

If +1/x=√2 find x²³+x¹⁹+x¹⁷+x³+x⁴+6​

Answer 1

Answer:

6.6

Step-by-step explanation:

1/x=√2=2^1/2

x=2^(-1/2)

x²=2⁻¹=1/2

x⁴=1/4

Now

x²³+x¹⁹+x¹⁷+x³+x⁴+6

=1/x(x²⁴+x²⁰+x¹⁸+x⁴) +x⁴+6

=√2*{ (x⁴)⁶ +(x⁴)⁵ +(x²)⁹ +x⁴) +x⁴ +6

=√2* { (1/4)⁶+(1/4)⁵ +(1/2)⁹+1/4) +1/4+6

=√2* ( 1/4⁶ +1/4⁵ +1/2⁹+1/4)+1/4+6

=√2*( 1/2¹²+1/2¹⁰+1/2⁹+1/2²)+1/4+6

=√2*1/2¹²( 1+2²+2³+2¹⁰)+1/4+6

=√2*1/2¹²(1+4+8+1024)+(1+24)/4

=√2*1/2¹²(1037)+25/4

= √2*1/2¹²(1037)+25/4

=√2*(1037)/4096+6.25

=1.41*1037/4096 +6.25

=0.35+6.25

=6.60