What is the answer to x-sqrt(x+1)=sqrt(4x-9) ?

The answer to x-sqrt(x+1)=sqrt(4x-9) is x\approx 2.31022…,x\approx 7.49502…

Solve for x: x-sqrt(x+1)=sqrt(4x-9)

The solution is x\approx 2.31022…,x\approx 7.49502…

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x - x + 1 = 4 x - 9

x \approx 2.31022 \dots, x \approx 7.49502 \dots

Solution steps

x - x + 1 = 4 x - 9

Remove square roots

4 x^{3} + 4 x^{2} = x^{4} - 6 x^{3} + 29 x^{2} - 60 x + 100

Solve

4 x^{3} + 4 x^{2} = x^{4} - 6 x^{3} + 29 x^{2} - 60 x + 100 : x \approx 2.31022 \dots, x \approx 7.49502 \dots

x \approx 2.31022 \dots, x \approx 7.49502 \dots

Verify Solutions:

x \approx 2.31022 \dots

True

, x \approx 7.49502 \dots

True

The solutions are

x \approx 2.31022 \dots, x \approx 7.49502 \dots

4 x - 2 = 10 x + 6

(2 x^{2} + 8)^{\frac{1}{4}} = x

4 x + 20 = x + 2

x = 24

What is the answer to x-sqrt(x+1)=sqrt(4x-9) ?
The answer to x-sqrt(x+1)=sqrt(4x-9) is x\approx 2.31022…,x\approx 7.49502…
Solve for x: x-sqrt(x+1)=sqrt(4x-9)
The solution is x\approx 2.31022…,x\approx 7.49502…