What are the solutions to the equation 76= 1/2 (h(h^2+3)) ?

The solutions to the equation 76= 1/2 (h(h^2+3)) are h\approx 5.14950…

Find the zeros of 76= 1/2 (h(h^2+3))

The zeros of 76= 1/2 (h(h^2+3)) are h\approx 5.14950…

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76 = \frac{1}{2} (h (h^{2} + 3))

h \approx 5.14950 \dots

Solution steps

76 = \frac{1}{2} (h (h^{2} + 3))

Multiply both sides by

2

152 = h (h^{2} + 3)

Expand

h (h^{2} + 3) : h^{3} + 3 h

152 = h^{3} + 3 h

Switch sides

h^{3} + 3 h = 152

Move

152

to the left side

h^{3} + 3 h - 152 = 0

Find one solution for

h^{3} + 3 h - 152 = 0

using Newton-Raphson:

h \approx 5.14950 \dots

Apply long division:

\frac{h ^{3} + 3 h - 152}{h - 5.14950 \dots} = h^{2} + 5.14950 \dots h + 29.51740 \dots

h^{2} + 5.14950 \dots h + 29.51740 \dots \approx 0

Find one solution for

h^{2} + 5.14950 \dots h + 29.51740 \dots = 0

using Newton-Raphson:

No Solution for

h \in R

The solution is

h \approx 5.14950 \dots

x^{2} = 8 x^{15}

4 x^{3} - 6 x^{2} - 20 x + 30 = 0

(x^{2} - 8 x + 15) (x + 1) = 0

x^{4} - 4 x^{3} + 7 x^{2} - 8 x + 10 = 0

2 - 3 - 2 x^{4} - 3 x - 16 + 2 x - 3 = x + 12, a

What are the solutions to the equation 76= 1/2 (h(h^2+3)) ?
The solutions to the equation 76= 1/2 (h(h^2+3)) are h\approx 5.14950…
Find the zeros of 76= 1/2 (h(h^2+3))
The zeros of 76= 1/2 (h(h^2+3)) are h\approx 5.14950…