What are the solutions to the equation a^6+a/2 =28 ?

The solutions to the equation a^6+a/2 =28 are a\approx 1.73347…,a\approx-1.75154…

Find the zeros of a^6+a/2 =28

The zeros of a^6+a/2 =28 are a\approx 1.73347…,a\approx-1.75154…

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a^{6} + \frac{a}{2} = 28

a \approx 1.73347 \dots, a \approx - 1.75154 \dots

Solution steps

a^{6} + \frac{a}{2} = 28

Multiply both sides by

2

2 a^{6} + a = 56

Move

56

to the left side

2 a^{6} + a - 56 = 0

Find one solution for

2 a^{6} + a - 56 = 0

using Newton-Raphson:

a \approx 1.73347 \dots

Apply long division:

\frac{2 a ^{6} + a - 56}{a - 1.73347 \dots} = 2 a^{5} + 3.46694 \dots a^{4} + 6.00985 \dots a^{3} + 10.41791 \dots a^{2} + 18.05917 \dots a + 32.30509 \dots

2 a^{5} + 3.46694 \dots a^{4} + 6.00985 \dots a^{3} + 10.41791 \dots a^{2} + 18.05917 \dots a + 32.30509 \dots \approx 0

Find one solution for

2 a^{5} + 3.46694 \dots a^{4} + 6.00985 \dots a^{3} + 10.41791 \dots a^{2} + 18.05917 \dots a + 32.30509 \dots = 0

using Newton-Raphson:

a \approx - 1.75154 \dots

Apply long division:

\frac{2 a ^{5} + 3.46694 \dots a ^{4} + 6.00985 \dots a ^{3} + 10.41791 \dots a ^{2} + 18.05917 \dots a + 32.30509 \dots}{a + 1.75154 \dots} = 2 a^{4} - 0.03615 \dots a^{3} + 6.07317 \dots a^{2} - 0.21954 \dots a + 18.44372 \dots

2 a^{4} - 0.03615 \dots a^{3} + 6.07317 \dots a^{2} - 0.21954 \dots a + 18.44372 \dots \approx 0

Find one solution for

2 a^{4} - 0.03615 \dots a^{3} + 6.07317 \dots a^{2} - 0.21954 \dots a + 18.44372 \dots = 0

using Newton-Raphson:

No Solution for

a \in R

The solutions are

a \approx 1.73347 \dots, a \approx - 1.75154 \dots

\frac{21 x ^{7}}{2} = 7

(x + 2) (x - 3) (x^{2} + x - 2) = 0

x^{6} = 16 x^{3}

x^{4} - 2 x^{2} = 35

4 y^{4} + 7 y^{2} - 36 = 0

What are the solutions to the equation a^6+a/2 =28 ?
The solutions to the equation a^6+a/2 =28 are a\approx 1.73347…,a\approx-1.75154…
Find the zeros of a^6+a/2 =28
The zeros of a^6+a/2 =28 are a\approx 1.73347…,a\approx-1.75154…