Question

Given that (1 - x) (1 + x + x² + x3 + x4) is 31/32 and x is a rational number, what is1 + x + x2 + x3 + x4 + x5?​

Answer 1

Answer: I hope this is helpful for you

Step-by-step explanation:

Answer 2

Given: (1 - x) (1 + x + x² + x³ + x⁴) = 31/32

It gives one solution x = 1/2.

Now before substituting let's reuse the given equation.

$(1 - x) (1 + x + x^2 + x^3 + x^4)\div (1-x) = \frac{31}{32} \div (1-x)$

$1 + x + x^2 + x^3 + x^4=\frac{31}{32} \div \frac{1}{2}$

∴ $1 + x + x^2 + x^3 + x^4=\frac{62}{32}$

We should add x⁵. It is 1/32.

∴ $1 + x + x^2 + x^3 + x^4 + x^5 = \frac{63}{32}$

For Your Information:

→ (1 - x) (1 + x + x² + x³ + x⁴) = 31/32

→ 1 - x⁵ = 31/32

→ x⁵ = 1/32

→ x⁵ = (1/2)⁵

→ Rational solution is x = 1/2