If x4-x3-x2-x-1-0 then the value of x5 is

We are given x4 + x3 + x2+ x + 1 = 0 #8658; x4 + x3 + x2+ x = 1 nbsp; —(1) Multiply throughout by x, x5 + x4 + x3 + x2 + x = 0 #8658;x5 + ...

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Standard X

Mathematics

Multiplying/Dividing a Positive Entity

if x4+x3+x2+x...

Question

if x⁴+x³+x²+x+1=0 then the value of x^{5 is}

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Solution

We are given x⁴+ x³+ x²+ x + 1 = 0

$\Rightarrow$ x⁴+ x³+ x²+ x = - 1 ---(1)

Multiply throughout by x,

x⁵ + x⁴ + x³ + x² + x = 0

$\Rightarrow$ x⁵ + (- 1) = 0, using (1)

$\Rightarrow$ x⁵ - 1 = 0

$\Rightarrow$ x⁵ = 1

Hence, the answer.

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if x4+x3+x2+x+1=0 then the value of x5 is

We are given x4 + x3 + x2+ x + 1 = 0 ⇒ x4 + x3 + x2+ x = - 1 ---(1) Multiply throughout by x, x5 + x4 + x3 + x2 + x = 0 ⇒x5 + (- 1) = 0, using (1) ⇒x5 - 1 = 0 ⇒x5 = 1 Hence, the answer.

if x⁴+x³+x²+x+1=0 then the value of x^{5 is}

We are given x⁴+ x³+ x²+ x + 1 = 0

$\Rightarrow$ x⁴+ x³+ x²+ x = - 1 ---(1)

Multiply throughout by x,

x⁵ + x⁴ + x³ + x² + x = 0

$\Rightarrow$ x⁵ + (- 1) = 0, using (1)

$\Rightarrow$ x⁵ - 1 = 0

$\Rightarrow$ x⁵ = 1

Hence, the answer.