What are the solutions to the equation a^8-a^7=5,a^1=3 ?

The solutions to the equation a^8-a^7=5,a^1=3 are a\approx 1.42306…,a\approx-1.12966…

Find the zeros of a^8-a^7=5,a^1=3

The zeros of a^8-a^7=5,a^1=3 are a\approx 1.42306…,a\approx-1.12966…

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a^{8} - a^{7} = 5, a^{1} = 3

a \approx 1.42306 \dots, a \approx - 1.12966 \dots

Solution steps

a^{8} - a^{7} = 5

Move

5

to the left side

a^{8} - a^{7} - 5 = 0

Find one solution for

a^{8} - a^{7} - 5 = 0

using Newton-Raphson:

a \approx 1.42306 \dots

Apply long division:

\frac{a ^{8} - a ^{7} - 5}{a - 1.42306 \dots} = a^{7} + 0.42306 \dots a^{6} + 0.60204 \dots a^{5} + 0.85674 \dots a^{4} + 1.21920 \dots a^{3} + 1.73499 \dots a^{2} + 2.46900 \dots a + 3.51355 \dots

a^{7} + 0.42306 \dots a^{6} + 0.60204 \dots a^{5} + 0.85674 \dots a^{4} + 1.21920 \dots a^{3} + 1.73499 \dots a^{2} + 2.46900 \dots a + 3.51355 \dots \approx 0

Find one solution for

a^{7} + 0.42306 \dots a^{6} + 0.60204 \dots a^{5} + 0.85674 \dots a^{4} + 1.21920 \dots a^{3} + 1.73499 \dots a^{2} + 2.46900 \dots a + 3.51355 \dots = 0

using Newton-Raphson:

a \approx - 1.12966 \dots

Apply long division:

\frac{a ^{7} + 0.42306 \dots a ^{6} + 0.60204 \dots a ^{5} + 0.85674 \dots a ^{4} + 1.21920 \dots a ^{3} + 1.73499 \dots a ^{2} + 2.46900 \dots a + 3.51355 \dots}{a + 1.12966 \dots} = a^{6} - 0.70660 \dots a^{5} + 1.40027 \dots a^{4} - 0.72510 \dots a^{3} + 2.03832 \dots a^{2} - 0.56763 \dots a + 3.11024 \dots

a^{6} - 0.70660 \dots a^{5} + 1.40027 \dots a^{4} - 0.72510 \dots a^{3} + 2.03832 \dots a^{2} - 0.56763 \dots a + 3.11024 \dots \approx 0

Find one solution for

a^{6} - 0.70660 \dots a^{5} + 1.40027 \dots a^{4} - 0.72510 \dots a^{3} + 2.03832 \dots a^{2} - 0.56763 \dots a + 3.11024 \dots = 0

using Newton-Raphson:

No Solution for

a \in R

The solutions are

a \approx 1.42306 \dots, a \approx - 1.12966 \dots

(x - 7)^{4} = 62 5^{7}

(2 x^{2} - 3)^{2} = 49

10 r + 1 = [1 + r]^{6}

1 - x^{9} = (1 - x) (1 + x + x^{2})

x^{4} - 81 = 0

What are the solutions to the equation a^8-a^7=5,a^1=3 ?
The solutions to the equation a^8-a^7=5,a^1=3 are a\approx 1.42306…,a\approx-1.12966…
Find the zeros of a^8-a^7=5,a^1=3
The zeros of a^8-a^7=5,a^1=3 are a\approx 1.42306…,a\approx-1.12966…