What is the answer to sqrt(x-4)= 1/(x^2-81) ?

The answer to sqrt(x-4)= 1/(x^2-81) is x\approx 9.02474…

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sqrt(x-4)= 1/(x^2-81)

x - 4 = \frac{1}{x ^{2} - 81}

x \approx 9.02474 \dots

Solution steps

x - 4 = \frac{1}{x ^{2} - 81}

Multiply both sides by

x^{2} - 81

x - 4 (x^{2} - 81) = \frac{1}{x ^{2} - 81} (x^{2} - 81)

Simplify

x - 4 (x^{2} - 81) = 1

Expand

x - 4 (x^{2} - 81) : x - 4 x^{2} - 81 x - 4

x - 4 x^{2} - 81 x - 4 = 1

Factor

x - 4 x^{2} - 81 x - 4 : (x + 9) (x - 9) x - 4

(x + 9) (x - 9) x - 4 = 1

Square both sides:

x^{5} - 4 x^{4} - 162 x^{3} + 648 x^{2} + 6561 x - 26244 = 1

x^{5} - 4 x^{4} - 162 x^{3} + 648 x^{2} + 6561 x - 26244 = 1

Solve

x^{5} - 4 x^{4} - 162 x^{3} + 648 x^{2} + 6561 x - 26244 = 1 : x \approx 4.00023 \dots, x \approx 9.02474 \dots, x \approx 8.97505 \dots

x \approx 4.00023 \dots, x \approx 9.02474 \dots, x \approx 8.97505 \dots

Verify Solutions:

x \approx 4.00023 \dots

False

, x \approx 9.02474 \dots

True

, x \approx 8.97505 \dots

False

The solution is

x \approx 9.02474 \dots

x + x = 16

1 = - 2 ln (2) + x

50 - 10 x = 2 x

p, x - 4000 = - 10 p

What is the answer to sqrt(x-4)= 1/(x^2-81) ?
The answer to sqrt(x-4)= 1/(x^2-81) is x\approx 9.02474…
Solve for x: sqrt(x-4)= 1/(x^2-81)
The solution is x\approx 9.02474…