What is the answer to sqrt(x+\sqrt{x+\sqrt{x+\sqrt{x)}}}=2 ?

The answer to sqrt(x+\sqrt{x+\sqrt{x+\sqrt{x)}}}=2 is x\approx 2.02852…

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sqrt(x+\sqrt{x+\sqrt{x+\sqrt{x)}}}=2

x + x + x + x = 2

x \approx 2.02852 \dots

Solution steps

x + x + x + x = 2

Remove square roots

x = x^{8} - 36 x^{7} + 550 x^{6} - 4646 x^{5} + 23685 x^{4} - 74530 x^{3} + 141377 x^{2} - 147968 x + 65536

Solve

x = x^{8} - 36 x^{7} + 550 x^{6} - 4646 x^{5} + 23685 x^{4} - 74530 x^{3} + 141377 x^{2} - 147968 x + 65536 : x \approx 2.02852 \dots, x \approx 2.23906 \dots, x \approx 2.70553 \dots, x \approx 3.06643 \dots, x \approx 5.68698 \dots, x \approx 6.03564 \dots, x \approx 7.01797 \dots, x \approx 7.21983 \dots

x \approx 2.02852 \dots, x \approx 2.23906 \dots, x \approx 2.70553 \dots, x \approx 3.06643 \dots, x \approx 5.68698 \dots, x \approx 6.03564 \dots, x \approx 7.01797 \dots, x \approx 7.21983 \dots

Verify Solutions:

x \approx 2.02852 \dots

True

, x \approx 2.23906 \dots

False

, x \approx 2.70553 \dots

False

, x \approx 3.06643 \dots

False

, x \approx 5.68698 \dots

False

, x \approx 6.03564 \dots

False

, x \approx 7.01797 \dots

False

, x \approx 7.21983 \dots

False

The solution is

x \approx 2.02852 \dots

y - 8 + 5 = 7

0 = - 3 3 x + 1 + 2

x^{2} - 2 x + 3 - x = 3 - x + 8

3 - 2 v + 17 = 20

What is the answer to sqrt(x+\sqrt{x+\sqrt{x+\sqrt{x)}}}=2 ?
The answer to sqrt(x+\sqrt{x+\sqrt{x+\sqrt{x)}}}=2 is x\approx 2.02852…
Solve for x: sqrt(x+\sqrt{x+\sqrt{x+\sqrt{x)}}}=2
The solution is x\approx 2.02852…