Find the solutions of the equation. 27x^{3}=(x+5)^{3}

Isa Trevino

Isa Trevino

Answered question

2021-10-02

Find the solutions of the equation.
27x3=(x+5)3

Answer & Explanation

Nathanael Webber

Nathanael Webber

Skilled2021-10-03Added 117 answers

Step 1
Given:
The equation 27x3=(x+5)3.
The solutions of the given equation can be obtained as,
(x+5)3=27x3
x3+3(x2×5)+3(x×52)+125=27x3
(as(a+b)3=a3+3a2b+3ab2+b3)
26x315x275x125=0
On solving the above cubic equation,
x=2.5, or x=0.96+0.1i or x=0.960.1i
Step 2
Hence, the solutions of the given equation are x=2.5, x=0.96+0.1i and x=0.960.1i .

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