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Solve the equation without using a calculator


(x^2-9x-1)^(10)+99x^(10)=10x^9(x^2-1)

Solve the equation without using a calculator (x^2-9x-1)^(10)+99x^(10)=10x^9(x^2-1)-example-1
User Aliopi
by
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1 Answer

3 votes

Answer:

  • x = 5 ± √26

-------------------------

Convert the given equation as below:


  • (x^2-9x-1)^(10)+99x^(10)=10x^9(x^2-1)

  • (x^2-9x-1)^(10)+99x^(10)=10x^9(x^2-9x-1)+10x^9(9x)

  • (x^2-9x-1)^(10)+99x^(10)=10x^9(x^2-9x-1)+90x^(10)

  • (x^2-9x-1)^(10)+9x^(10)=10x^9(x^2-9x-1)

  • (x^2-9x-1)^(10)-9x^9(x^2-9x-1)=x^9(x^2-9x-1)-9x^9x

Let's substitute x² - 9x - 1 = t, then the equation is:


  • t^9t-9x^9t=x^9t-9x^9x

Comparing both sides, we see that x = t, so:

  • x² - 9x - 1 = x
  • x² - 10x - 1 = 0

Solving this quadratic equation we get:

  • x = 5 ± √26
User Sugaryourcoffee
by
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