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Popular >

3^2+y^3=16y+1

Solution

3^{2} + y^{3} = 16 y + 1

Solution

y \approx 0.50820 \dots, y \approx 3.72161 \dots, y \approx - 4.22981 \dots

Solution steps

3^{2} + y^{3} = 16 y + 1

Expand

3^{2} + y^{3} : 9 + y^{3}

9 + y^{3} = 16 y + 1

Move

1

to the left side

y^{3} + 8 = 16 y

Move

16 y

to the left side

y^{3} + 8 - 16 y = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

y^{3} - 16 y + 8 = 0

Find one solution for

y^{3} - 16 y + 8 = 0

using Newton-Raphson:

y \approx 0.50820 \dots

Apply long division:

\frac{y ^{3} - 16 y + 8}{y - 0.50820 \dots} = y^{2} + 0.50820 \dots y - 15.74172 \dots

y^{2} + 0.50820 \dots y - 15.74172 \dots \approx 0

Find one solution for

y^{2} + 0.50820 \dots y - 15.74172 \dots = 0

using Newton-Raphson:

y \approx 3.72161 \dots

Apply long division:

\frac{y ^{2} + 0.50820 \dots y - 15.74172 \dots}{y - 3.72161 \dots} = y + 4.22981 \dots

y + 4.22981 \dots \approx 0

y \approx - 4.22981 \dots

The solutions are

y \approx 0.50820 \dots, y \approx 3.72161 \dots, y \approx - 4.22981 \dots

Popular Examples

b^{4} + 9 b^{2} + 18 = 0

solvefor p,p^4-q^3=infinity solve for

p, p^{4} - q^{3} = \infty

- 2 x^{4} + 9 = 2 x + 1

39 = p^{3} + 32

x^3+x^2+17x-15=0

x^{3} + x^{2} + 17 x - 15 = 0