What is the answer to a=sqrt(x+3)+sqrt(3x+1) ?

The answer to a=sqrt(x+3)+sqrt(3x+1) is x=(2a^2+2+asqrt(3a^2+16))/2 ,x=(2a^2+2-asqrt(3a^2+16))/2

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a=sqrt(x+3)+sqrt(3x+1)

a = x + 3 + 3 x + 1

x = \frac{2 a ^{2} + 2 + a 3 a ^{2} + 16}{2}, x = \frac{2 a ^{2} + 2 - a 3 a ^{2} + 16}{2}

Solution steps

a = x + 3 + 3 x + 1

Remove square roots

12 a^{2} x + 4 a^{2} = 4 a^{2} x + 4 x^{2} - 8 x - 4 a^{2} + a^{4} + 4

Solve

12 a^{2} x + 4 a^{2} = 4 a^{2} x + 4 x^{2} - 8 x - 4 a^{2} + a^{4} + 4 : x = \frac{2 a ^{2} + 2 + a 3 a ^{2} + 16}{2}, x = \frac{2 a ^{2} + 2 - a 3 a ^{2} + 16}{2}

x = \frac{2 a ^{2} + 2 + a 3 a ^{2} + 16}{2}, x = \frac{2 a ^{2} + 2 - a 3 a ^{2} + 16}{2}

Verify Solutions:

x = \frac{2 a ^{2} + 2 + a 3 a ^{2} + 16}{2}

True

, x = \frac{2 a ^{2} + 2 - a 3 a ^{2} + 16}{2}

True

The solutions are

x = \frac{2 a ^{2} + 2 + a 3 a ^{2} + 16}{2}, x = \frac{2 a ^{2} + 2 - a 3 a ^{2} + 16}{2}

2 x + 3 - x + 2 = 2

x = (12 + 4 x)^{\frac{1}{2}}

a, a + b = 2009

x + 10 - 1 = - 3

What is the answer to a=sqrt(x+3)+sqrt(3x+1) ?
The answer to a=sqrt(x+3)+sqrt(3x+1) is x=(2a^2+2+asqrt(3a^2+16))/2 ,x=(2a^2+2-asqrt(3a^2+16))/2