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

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

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

The solution is x=1,x=-2,x=2,x=-3

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sqrt(3x^2+3x-2)+sqrt(2x^2+2x-3)=x^2+x+1

Solution

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

Solution

x = 1, x = - 2, x = 2, x = - 3

Solution steps

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

Remove square roots

8 x^{6} + 24 x^{5} + 28 x^{4} + 16 x^{3} - 12 x^{2} - 16 x - 12 = x^{8} + 4 x^{7} + 8 x^{6} + 10 x^{5} + 8 x^{4} + 4 x^{3} + x^{2}

Add

2

to both sides

3 x^{2} + 3 x - 2 + 2 = x^{4} + 2 x^{3} + 5 x^{2} - 2 2 x^{2} + 2 x - 3 x^{2} + 4 x - 2 2 x^{2} + 2 x - 3 x - 2 2 x^{2} + 2 x - 3 - 2 + 2

Simplify

3 x^{2} + 3 x = x^{4} + 2 x^{3} + 5 x^{2} - 2 2 x^{2} + 2 x - 3 x^{2} + 4 x - 2 2 x^{2} + 2 x - 3 x - 2 2 x^{2} + 2 x - 3

Switch sides

x^{4} + 2 x^{3} + 5 x^{2} - 2 2 x^{2} + 2 x - 3 x^{2} + 4 x - 2 2 x^{2} + 2 x - 3 x - 2 2 x^{2} + 2 x - 3 = 3 x^{2} + 3 x

Move

x^{4}

to the right side

2 x^{3} + 5 x^{2} - 2 2 x^{2} + 2 x - 3 x^{2} + 4 x - 2 2 x^{2} + 2 x - 3 x - 2 2 x^{2} + 2 x - 3 = 3 x^{2} + 3 x - x^{4}

Move

2 x^{3}

to the right side

5 x^{2} - 2 2 x^{2} + 2 x - 3 x^{2} + 4 x - 2 2 x^{2} + 2 x - 3 x - 2 2 x^{2} + 2 x - 3 = 3 x^{2} + 3 x - x^{4} - 2 x^{3}

Move

5 x^{2}

to the right side

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

Move

4 x

to the right side

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

Factor

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

- 2 2 x^{2} + 2 x - 3 (x^{2} + x + 1) = - x^{4} - 2 x^{3} - 2 x^{2} - x

Solve

8 x^{6} + 24 x^{5} + 28 x^{4} + 16 x^{3} - 12 x^{2} - 16 x - 12 = x^{8} + 4 x^{7} + 8 x^{6} + 10 x^{5} + 8 x^{4} + 4 x^{3} + x^{2} : x = 1, x = - 2, x = 2, x = - 3

x = 1, x = - 2, x = 2, x = - 3

Verify Solutions:

x = 1

True

, x = - 2

True

, x = 2

True

, x = - 3

True

The solutions are

x = 1, x = - 2, x = 2, x = - 3

Popular Examples

solvefor x,x^{2/3}+y^{2/3}=a^{2/3}solve for

x, x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}

sqrt(x+2)=sqrt(2x+1)

x + 2 = 2 x + 1

x-1-2sqrt(x+1)=0

x - 1 - 2 x + 1 = 0

(x-2)^{2/3}+(x-2)^{1/3}-2=0

(x - 2)^{\frac{2}{3}} + (x - 2)^{\frac{1}{3}} - 2 = 0

sqrt(3x)-sqrt(27)=0

3 x - 27 = 0

Frequently Asked Questions (FAQ)

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