What are the solutions to the equation (x+1)^2=3(x-1)^2 ?

The solutions to the equation (x+1)^2=3(x-1)^2 are x=2-sqrt(3),x=2+sqrt(3)

Find the zeros of (x+1)^2=3(x-1)^2

The zeros of (x+1)^2=3(x-1)^2 are x=2-sqrt(3),x=2+sqrt(3)

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

x = 2 - 3, x = 2 + 3

Decimal Notation

x = 0.26794 \dots, x = 3.73205 \dots

Solution steps

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

Expand

(x + 1)^{2} : x^{2} + 2 x + 1

Expand

3 (x - 1)^{2} : 3 x^{2} - 6 x + 3

x^{2} + 2 x + 1 = 3 x^{2} - 6 x + 3

Move

3

to the left side

x^{2} + 2 x - 2 = 3 x^{2} - 6 x

Move

6 x

to the left side

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

Move

3 x^{2}

to the left side

- 2 x^{2} + 8 x - 2 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 ( - 2 ) ( - 2 )}{2 ( - 2 )}

8^{2} - 4 (- 2) (- 2) = 43

x_{1, 2} = \frac{- 8 \pm 4 3}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- 8 + 4 3}{2 ( - 2 )}, x_{2} = \frac{- 8 - 4 3}{2 ( - 2 )}

x = \frac{- 8 + 4 3}{2 ( - 2 )} : 2 - 3

x = \frac{- 8 - 4 3}{2 ( - 2 )} : 2 + 3

The solutions to the quadratic equation are:

x = 2 - 3, x = 2 + 3

x^{2} - 5 = 8 - 2 x^{2}

5 x (x - 2) = 6 + 3 x

x, x^{2} - 15 - m (2 x - 8) = 0

x^{2} - 5 x + 3 = 0

5 x^{2} + 10 x + 8 = 0

What are the solutions to the equation (x+1)^2=3(x-1)^2 ?
The solutions to the equation (x+1)^2=3(x-1)^2 are x=2-sqrt(3),x=2+sqrt(3)
Find the zeros of (x+1)^2=3(x-1)^2
The zeros of (x+1)^2=3(x-1)^2 are x=2-sqrt(3),x=2+sqrt(3)