What are the solutions to the equation 10r+1=[1+r]^6 ?

The solutions to the equation 10r+1=[1+r]^6 are r=0,r\approx 0.20279…

Find the zeros of 10r+1=[1+r]^6

The zeros of 10r+1=[1+r]^6 are r=0,r\approx 0.20279…

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

r = 0, r \approx 0.20279 \dots

Solution steps

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

Expand

(1 + r)^{6} : 1 + 6 r + 15 r^{2} + 20 r^{3} + 15 r^{4} + 6 r^{5} + r^{6}

10 r + 1 = 1 + 6 r + 15 r^{2} + 20 r^{3} + 15 r^{4} + 6 r^{5} + r^{6}

Switch sides

1 + 6 r + 15 r^{2} + 20 r^{3} + 15 r^{4} + 6 r^{5} + r^{6} = 10 r + 1

Move

1

to the left side

r^{6} + 6 r^{5} + 15 r^{4} + 20 r^{3} + 15 r^{2} + 6 r = 10 r

Move

10 r

to the left side

r^{6} + 6 r^{5} + 15 r^{4} + 20 r^{3} + 15 r^{2} - 4 r = 0

Factor

r^{6} + 6 r^{5} + 15 r^{4} + 20 r^{3} + 15 r^{2} - 4 r : r (r^{5} + 6 r^{4} + 15 r^{3} + 20 r^{2} + 15 r - 4)

r (r^{5} + 6 r^{4} + 15 r^{3} + 20 r^{2} + 15 r - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

r = 0 or r^{5} + 6 r^{4} + 15 r^{3} + 20 r^{2} + 15 r - 4 = 0

Solve

r^{5} + 6 r^{4} + 15 r^{3} + 20 r^{2} + 15 r - 4 = 0 : r \approx 0.20279 \dots

The solutions are

r = 0, r \approx 0.20279 \dots

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

x^{4} - 81 = 0

x^{4} - 6 x^{2} + 5 = 0

(x) = 3 x^{3} + x^{2} - 22 x + 9

280 xx - x x^{7} - x = 250

What are the solutions to the equation 10r+1=[1+r]^6 ?
The solutions to the equation 10r+1=[1+r]^6 are r=0,r\approx 0.20279…
Find the zeros of 10r+1=[1+r]^6
The zeros of 10r+1=[1+r]^6 are r=0,r\approx 0.20279…