Question #a5653

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Question #a5653

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Answer 1 · 2018-02-02T05:52:00

$x = 4 \pm 2 \sqrt{2}$ $x=4+-2sqrt(2)$

Explanation:

Square both sides. ${(x + y)}^{2} = x^{2} + 2 x y + y^{2}$ $(x+y)^2 = x^2 +2xy+y^2$

${(\sqrt{3 x - 1} - \sqrt{x - 1})}^{2} = 2^{2}$ $(sqrt(3x-1) - sqrt(x-1))^2 = 2^2$

$3 x - 1 - 2 \sqrt{(3 x - 1) \cdot (x - 1)} + x - 1 = 4$ $3x-1-2sqrt((3x-1)*(x-1))+x-1=4$

Combine like terms and multiply.
$4 x - 2 - 2 \sqrt{3 x^{2} - 4 x + 1} = 4$ $4x-2-2sqrt(3x^2-4x+1)=4$

3.Divide by $2$ $2$
$2 x - 1 - \sqrt{3 x^{2} - 4 x + 1} = 2$ $2x-1-sqrt(3x^2-4x+1)=2$

4.Subtract $[2 x - 1]$ $[2x-1]$ from both sides
$- \sqrt{3 x^{2} - 4 x + 1} = 2 - 2 x + 1$ $-sqrt(3x^2-4x+1)=2-2x+1$

$5$ $5$ . Combine like terms and multiply by $(- 1)$ $(-1)$
$\sqrt{3 x^{2} - 4 x + 1} = 2 x - 3$ $sqrt(3x^2-4x+1)=2x-3$

6.Square both sides.
$3 x^{2} - 4 x + 1 = 4 x^{2} - 12 x + 9$ $3x^2-4x+1=4x^2-12x+9$

7.subtract $[4 x^{2} - 12 x + 9]$ $[4x^2-12x+9]$ and combine like terms.
$- x^{2} + 8 x - 8 = 0$ $-x^2+8x-8=0$

$8$ $8$ . Use the quadratic formula.
$x = \frac{- 8 + \sqrt{64 - 32}}{- 2}, x = \frac{- 8 - \sqrt{64 - 32}}{- 2}$ $x=(-8+sqrt(64-32))/-2,x=(-8-sqrt(64-32))/-2$

9.Simplify
$x = 4 + 2 \sqrt{2}, 4 - 2 \sqrt{2} .$ $x=4+2sqrt(2)," "4-2sqrt(2).$

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Question #a5653

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