What is the answer to (x+1)sqrt(x^2-2x+3)=x^2+1 ?

The answer to (x+1)sqrt(x^2-2x+3)=x^2+1 is x=1-sqrt(2),x=1+sqrt(2)

Solve for x: (x+1)sqrt(x^2-2x+3)=x^2+1

The solution is x=1-sqrt(2),x=1+sqrt(2)

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(x + 1) x^{2} - 2 x + 3 = x^{2} + 1

x = 1 - 2, x = 1 + 2

Decimal

x = - 0.41421 \dots, x = 2.41421 \dots

Solution steps

(x + 1) x^{2} - 2 x + 3 = x^{2} + 1

Square both sides:

x^{4} + 4 x + 3 = x^{4} + 2 x^{2} + 1

x^{4} + 4 x + 3 = x^{4} + 2 x^{2} + 1

Solve

x^{4} + 4 x + 3 = x^{4} + 2 x^{2} + 1 : x = 1 - 2, x = 1 + 2

x = 1 - 2, x = 1 + 2

Verify Solutions:

x = 1 - 2

True

, x = 1 + 2

True

The solutions are

x = 1 - 2, x = 1 + 2

3 (2 x + 4)^{\frac{4}{3}} = 48

y = 2 y^{\frac{1}{2}} + 15

4 3 h - 2 = 0

- x + 2 + - 3 x + 4 = - 2

x + 5 x - 10 = 8

What is the answer to (x+1)sqrt(x^2-2x+3)=x^2+1 ?
The answer to (x+1)sqrt(x^2-2x+3)=x^2+1 is x=1-sqrt(2),x=1+sqrt(2)
Solve for x: (x+1)sqrt(x^2-2x+3)=x^2+1
The solution is x=1-sqrt(2),x=1+sqrt(2)